diff --git a/src/language/modules/SchemeModule.cpp b/src/language/modules/SchemeModule.cpp
index c724e1674415b1a2be0c8848f0a9cf923bd24363..e4b52dc2277b95381213bff69af42749783fb655 100644
--- a/src/language/modules/SchemeModule.cpp
+++ b/src/language/modules/SchemeModule.cpp
@@ -11,6 +11,7 @@
 #include <language/utils/TypeDescriptor.hpp>
 #include <mesh/Connectivity.hpp>
 #include <mesh/IBoundaryDescriptor.hpp>
+#include <mesh/IZoneDescriptor.hpp>
 #include <mesh/Mesh.hpp>
 #include <mesh/MeshData.hpp>
 #include <mesh/MeshDataManager.hpp>
@@ -158,6 +159,55 @@ SchemeModule::SchemeModule()
 
       ));
 
+  this->_addBuiltinFunction("interpolate",
+                            std::make_shared<BuiltinFunctionEmbedder<std::shared_ptr<
+                              const IDiscreteFunction>(std::shared_ptr<const IMesh>,
+                                                       const std::vector<std::shared_ptr<const IZoneDescriptor>>&,
+                                                       std::shared_ptr<const IDiscreteFunctionDescriptor>,
+                                                       const std::vector<FunctionSymbolId>&)>>(
+                              [](std::shared_ptr<const IMesh> mesh,
+                                 const std::vector<std::shared_ptr<const IZoneDescriptor>>& interpolation_zone_list,
+                                 std::shared_ptr<const IDiscreteFunctionDescriptor> discrete_function_descriptor,
+                                 const std::vector<FunctionSymbolId>& function_id_list)
+                                -> std::shared_ptr<const IDiscreteFunction> {
+                                return DiscreteFunctionVectorInterpoler{mesh, interpolation_zone_list,
+                                                                        discrete_function_descriptor, function_id_list}
+                                  .interpolate();
+                              }
+
+                              ));
+
+  this->_addBuiltinFunction("interpolate",
+                            std::make_shared<BuiltinFunctionEmbedder<std::shared_ptr<
+                              const IDiscreteFunction>(std::shared_ptr<const IMesh>,
+                                                       const std::vector<std::shared_ptr<const IZoneDescriptor>>&,
+                                                       std::shared_ptr<const IDiscreteFunctionDescriptor>,
+                                                       const FunctionSymbolId&)>>(
+                              [](std::shared_ptr<const IMesh> mesh,
+                                 const std::vector<std::shared_ptr<const IZoneDescriptor>>& interpolation_zone_list,
+                                 std::shared_ptr<const IDiscreteFunctionDescriptor> discrete_function_descriptor,
+                                 const FunctionSymbolId& function_id) -> std::shared_ptr<const IDiscreteFunction> {
+                                switch (discrete_function_descriptor->type()) {
+                                case DiscreteFunctionType::P0: {
+                                  return DiscreteFunctionInterpoler{mesh, interpolation_zone_list,
+                                                                    discrete_function_descriptor, function_id}
+                                    .interpolate();
+                                }
+                                case DiscreteFunctionType::P0Vector: {
+                                  return DiscreteFunctionVectorInterpoler{mesh,
+                                                                          interpolation_zone_list,
+                                                                          discrete_function_descriptor,
+                                                                          {function_id}}
+                                    .interpolate();
+                                }
+                                default: {
+                                  throw NormalError("invalid function descriptor type");
+                                }
+                                }
+                              }
+
+                              ));
+
   this->_addBuiltinFunction("randomizeMesh",
                             std::make_shared<BuiltinFunctionEmbedder<std::shared_ptr<
                               const IMesh>(std::shared_ptr<const IMesh>,
diff --git a/src/scheme/DiscreteFunctionInterpoler.cpp b/src/scheme/DiscreteFunctionInterpoler.cpp
index c39b6ee9d7020b1ffee3582ee36bd461a0c03435..daf7646ee266c7c874c17b6b7403388fc33c3ce6 100644
--- a/src/scheme/DiscreteFunctionInterpoler.cpp
+++ b/src/scheme/DiscreteFunctionInterpoler.cpp
@@ -1,20 +1,82 @@
 #include <scheme/DiscreteFunctionInterpoler.hpp>
 
 #include <language/utils/InterpolateItemValue.hpp>
+#include <mesh/MeshCellZone.hpp>
 #include <scheme/DiscreteFunctionP0.hpp>
 #include <utils/Exceptions.hpp>
 
 template <size_t Dimension, typename DataType, typename ValueType>
 std::shared_ptr<IDiscreteFunction>
-DiscreteFunctionInterpoler::_interpolate() const
+DiscreteFunctionInterpoler::_interpolateOnZoneList() const
+{
+  static_assert(std::is_convertible_v<DataType, ValueType>);
+  Assert(m_zone_list.size() > 0, "no zone list provided");
+
+  std::shared_ptr p_mesh  = std::dynamic_pointer_cast<const Mesh<Connectivity<Dimension>>>(m_mesh);
+  using MeshDataType      = MeshData<Dimension>;
+  MeshDataType& mesh_data = MeshDataManager::instance().getMeshData(*p_mesh);
+
+  CellValue<bool> is_in_zone{p_mesh->connectivity()};
+  is_in_zone.fill(false);
+
+  size_t number_of_cells = 0;
+  for (const auto& zone : m_zone_list) {
+    auto mesh_cell_zone   = getMeshCellZone(*p_mesh, *zone);
+    const auto& cell_list = mesh_cell_zone.cellList();
+    for (size_t i_cell = 0; i_cell < cell_list.size(); ++i_cell) {
+      const CellId cell_id = cell_list[i_cell];
+      if (is_in_zone[cell_id]) {
+        std::ostringstream os;
+        os << "cell " << cell_id << " (number " << p_mesh->connectivity().cellNumber()[cell_id]
+           << ") is present multiple times in zone list";
+        throw NormalError(os.str());
+      }
+      ++number_of_cells;
+      is_in_zone[cell_id] = true;
+    }
+  }
+
+  Array<CellId> zone_cell_list{number_of_cells};
+  {
+    size_t i_cell = 0;
+    for (CellId cell_id = 0; cell_id < p_mesh->numberOfCells(); ++cell_id) {
+      if (is_in_zone[cell_id]) {
+        zone_cell_list[i_cell++] = cell_id;
+      }
+    }
+  }
+
+  Array<const DataType> array =
+    InterpolateItemValue<DataType(TinyVector<Dimension>)>::template interpolate<ItemType::cell>(m_function_id,
+                                                                                                mesh_data.xj(),
+                                                                                                zone_cell_list);
+
+  CellValue<ValueType> cell_value{p_mesh->connectivity()};
+  if constexpr (is_tiny_vector_v<ValueType> or is_tiny_matrix_v<ValueType>) {
+    cell_value.fill(zero);
+  } else {
+    cell_value.fill(0);
+  }
+
+  parallel_for(
+    zone_cell_list.size(), PUGS_LAMBDA(const size_t i_cell) { cell_value[zone_cell_list[i_cell]] = array[i_cell]; });
+
+  return std::make_shared<DiscreteFunctionP0<Dimension, ValueType>>(p_mesh, cell_value);
+}
+
+template <size_t Dimension, typename DataType, typename ValueType>
+std::shared_ptr<IDiscreteFunction>
+DiscreteFunctionInterpoler::_interpolateGlobally() const
 {
-  std::shared_ptr mesh    = std::dynamic_pointer_cast<const Mesh<Connectivity<Dimension>>>(m_mesh);
+  Assert(m_zone_list.size() == 0, "invalid call when zones are defined");
+
+  std::shared_ptr p_mesh  = std::dynamic_pointer_cast<const Mesh<Connectivity<Dimension>>>(m_mesh);
   using MeshDataType      = MeshData<Dimension>;
-  MeshDataType& mesh_data = MeshDataManager::instance().getMeshData(*mesh);
+  MeshDataType& mesh_data = MeshDataManager::instance().getMeshData(*p_mesh);
 
   if constexpr (std::is_same_v<DataType, ValueType>) {
     return std::make_shared<
-      DiscreteFunctionP0<Dimension, ValueType>>(mesh,
+      DiscreteFunctionP0<Dimension, ValueType>>(p_mesh,
                                                 InterpolateItemValue<DataType(TinyVector<Dimension>)>::
                                                   template interpolate<ItemType::cell>(m_function_id, mesh_data.xj()));
   } else {
@@ -24,12 +86,23 @@ DiscreteFunctionInterpoler::_interpolate() const
       InterpolateItemValue<DataType(TinyVector<Dimension>)>::template interpolate<ItemType::cell>(m_function_id,
                                                                                                   mesh_data.xj());
 
-    CellValue<ValueType> cell_value{mesh->connectivity()};
+    CellValue<ValueType> cell_value{p_mesh->connectivity()};
 
     parallel_for(
-      mesh->numberOfCells(), PUGS_LAMBDA(const CellId cell_id) { cell_value[cell_id] = cell_data[cell_id]; });
+      p_mesh->numberOfCells(), PUGS_LAMBDA(const CellId cell_id) { cell_value[cell_id] = cell_data[cell_id]; });
 
-    return std::make_shared<DiscreteFunctionP0<Dimension, ValueType>>(mesh, cell_value);
+    return std::make_shared<DiscreteFunctionP0<Dimension, ValueType>>(p_mesh, cell_value);
+  }
+}
+
+template <size_t Dimension, typename DataType, typename ValueType>
+std::shared_ptr<IDiscreteFunction>
+DiscreteFunctionInterpoler::_interpolate() const
+{
+  if (m_zone_list.size() == 0) {
+    return this->_interpolateGlobally<Dimension, DataType, ValueType>();
+  } else {
+    return this->_interpolateOnZoneList<Dimension, DataType, ValueType>();
   }
 }
 
diff --git a/src/scheme/DiscreteFunctionInterpoler.hpp b/src/scheme/DiscreteFunctionInterpoler.hpp
index e5724e3fec3ea75098772827537a1267f68328b7..295c2fd9a540269bf484f485716131b1346964e1 100644
--- a/src/scheme/DiscreteFunctionInterpoler.hpp
+++ b/src/scheme/DiscreteFunctionInterpoler.hpp
@@ -3,6 +3,7 @@
 
 #include <language/utils/FunctionSymbolId.hpp>
 #include <mesh/IMesh.hpp>
+#include <mesh/IZoneDescriptor.hpp>
 #include <scheme/IDiscreteFunction.hpp>
 #include <scheme/IDiscreteFunctionDescriptor.hpp>
 
@@ -12,9 +13,16 @@ class DiscreteFunctionInterpoler
 {
  private:
   std::shared_ptr<const IMesh> m_mesh;
+  const std::vector<std::shared_ptr<const IZoneDescriptor>> m_zone_list;
   std::shared_ptr<const IDiscreteFunctionDescriptor> m_discrete_function_descriptor;
   const FunctionSymbolId m_function_id;
 
+  template <size_t Dimension, typename DataType, typename ValueType = DataType>
+  std::shared_ptr<IDiscreteFunction> _interpolateOnZoneList() const;
+
+  template <size_t Dimension, typename DataType, typename ValueType = DataType>
+  std::shared_ptr<IDiscreteFunction> _interpolateGlobally() const;
+
   template <size_t Dimension, typename DataType, typename ValueType = DataType>
   std::shared_ptr<IDiscreteFunction> _interpolate() const;
 
@@ -30,6 +38,16 @@ class DiscreteFunctionInterpoler
     : m_mesh{mesh}, m_discrete_function_descriptor{discrete_function_descriptor}, m_function_id{function_id}
   {}
 
+  DiscreteFunctionInterpoler(const std::shared_ptr<const IMesh>& mesh,
+                             const std::vector<std::shared_ptr<const IZoneDescriptor>>& zone_list,
+                             const std::shared_ptr<const IDiscreteFunctionDescriptor>& discrete_function_descriptor,
+                             const FunctionSymbolId& function_id)
+    : m_mesh{mesh},
+      m_zone_list{zone_list},
+      m_discrete_function_descriptor{discrete_function_descriptor},
+      m_function_id{function_id}
+  {}
+
   DiscreteFunctionInterpoler(const DiscreteFunctionInterpoler&) = delete;
   DiscreteFunctionInterpoler(DiscreteFunctionInterpoler&&)      = delete;
 
diff --git a/src/scheme/DiscreteFunctionVectorInterpoler.cpp b/src/scheme/DiscreteFunctionVectorInterpoler.cpp
index 98d6513c9a896b81d8e6909e057a8300b66d6dc7..128c735e4ae8e158f3dc42bf3d5ed47b17ac3fb5 100644
--- a/src/scheme/DiscreteFunctionVectorInterpoler.cpp
+++ b/src/scheme/DiscreteFunctionVectorInterpoler.cpp
@@ -1,22 +1,94 @@
 #include <scheme/DiscreteFunctionVectorInterpoler.hpp>
 
 #include <language/utils/InterpolateItemArray.hpp>
+#include <mesh/MeshCellZone.hpp>
 #include <scheme/DiscreteFunctionP0Vector.hpp>
 #include <utils/Exceptions.hpp>
 
 template <size_t Dimension, typename DataType>
 std::shared_ptr<IDiscreteFunction>
-DiscreteFunctionVectorInterpoler::_interpolate() const
+DiscreteFunctionVectorInterpoler::_interpolateOnZoneList() const
 {
-  std::shared_ptr mesh = std::dynamic_pointer_cast<const Mesh<Connectivity<Dimension>>>(m_mesh);
+  Assert(m_zone_list.size() > 0, "no zone list provided");
 
+  std::shared_ptr p_mesh  = std::dynamic_pointer_cast<const Mesh<Connectivity<Dimension>>>(m_mesh);
   using MeshDataType      = MeshData<Dimension>;
-  MeshDataType& mesh_data = MeshDataManager::instance().getMeshData(*mesh);
+  MeshDataType& mesh_data = MeshDataManager::instance().getMeshData(*p_mesh);
+
+  CellValue<bool> is_in_zone{p_mesh->connectivity()};
+  is_in_zone.fill(false);
+
+  size_t number_of_cells = 0;
+  for (const auto& zone : m_zone_list) {
+    auto mesh_cell_zone   = getMeshCellZone(*p_mesh, *zone);
+    const auto& cell_list = mesh_cell_zone.cellList();
+    for (size_t i_cell = 0; i_cell < cell_list.size(); ++i_cell) {
+      const CellId cell_id = cell_list[i_cell];
+      if (is_in_zone[cell_id]) {
+        std::ostringstream os;
+        os << "cell " << cell_id << " (number " << p_mesh->connectivity().cellNumber()[cell_id]
+           << ") is present multiple times in zone list";
+        throw NormalError(os.str());
+      }
+      ++number_of_cells;
+      is_in_zone[cell_id] = true;
+    }
+  }
+
+  Array<CellId> zone_cell_list{number_of_cells};
+  {
+    size_t i_cell = 0;
+    for (CellId cell_id = 0; cell_id < p_mesh->numberOfCells(); ++cell_id) {
+      if (is_in_zone[cell_id]) {
+        zone_cell_list[i_cell++] = cell_id;
+      }
+    }
+  }
+
+  Table<const DataType> table =
+    InterpolateItemArray<DataType(TinyVector<Dimension>)>::template interpolate<ItemType::cell>(m_function_id_list,
+                                                                                                mesh_data.xj(),
+                                                                                                zone_cell_list);
+
+  CellArray<DataType> cell_array{p_mesh->connectivity(), m_function_id_list.size()};
+  cell_array.fill(0);
+
+  parallel_for(
+    zone_cell_list.size(), PUGS_LAMBDA(const size_t i_cell) {
+      for (size_t i = 0; i < table.numberOfColumns(); ++i) {
+        cell_array[zone_cell_list[i_cell]][i] = table(i_cell, i);
+      }
+    });
+
+  return std::make_shared<DiscreteFunctionP0Vector<Dimension, DataType>>(p_mesh, cell_array);
+}
+
+template <size_t Dimension, typename DataType>
+std::shared_ptr<IDiscreteFunction>
+DiscreteFunctionVectorInterpoler::_interpolateGlobally() const
+{
+  Assert(m_zone_list.size() == 0, "invalid call when zones are defined");
+
+  std::shared_ptr p_mesh = std::dynamic_pointer_cast<const Mesh<Connectivity<Dimension>>>(m_mesh);
+
+  using MeshDataType      = MeshData<Dimension>;
+  MeshDataType& mesh_data = MeshDataManager::instance().getMeshData(*p_mesh);
 
   return std::make_shared<
-    DiscreteFunctionP0Vector<Dimension, DataType>>(mesh, InterpolateItemArray<DataType(TinyVector<Dimension>)>::
-                                                           template interpolate<ItemType::cell>(m_function_id_list,
-                                                                                                mesh_data.xj()));
+    DiscreteFunctionP0Vector<Dimension, DataType>>(p_mesh, InterpolateItemArray<DataType(TinyVector<Dimension>)>::
+                                                             template interpolate<ItemType::cell>(m_function_id_list,
+                                                                                                  mesh_data.xj()));
+}
+
+template <size_t Dimension, typename DataType>
+std::shared_ptr<IDiscreteFunction>
+DiscreteFunctionVectorInterpoler::_interpolate() const
+{
+  if (m_zone_list.size() == 0) {
+    return this->_interpolateGlobally<Dimension, DataType>();
+  } else {
+    return this->_interpolateOnZoneList<Dimension, DataType>();
+  }
 }
 
 template <size_t Dimension>
diff --git a/src/scheme/DiscreteFunctionVectorInterpoler.hpp b/src/scheme/DiscreteFunctionVectorInterpoler.hpp
index 093f290c40b99dc7c3c8f6db1ab32cbae10dfcb2..4bd917264fcfdb8992d6096db824bc17951c2603 100644
--- a/src/scheme/DiscreteFunctionVectorInterpoler.hpp
+++ b/src/scheme/DiscreteFunctionVectorInterpoler.hpp
@@ -3,6 +3,7 @@
 
 #include <language/utils/FunctionSymbolId.hpp>
 #include <mesh/IMesh.hpp>
+#include <mesh/IZoneDescriptor.hpp>
 #include <scheme/IDiscreteFunction.hpp>
 #include <scheme/IDiscreteFunctionDescriptor.hpp>
 
@@ -13,9 +14,16 @@ class DiscreteFunctionVectorInterpoler
 {
  private:
   std::shared_ptr<const IMesh> m_mesh;
+  const std::vector<std::shared_ptr<const IZoneDescriptor>> m_zone_list;
   std::shared_ptr<const IDiscreteFunctionDescriptor> m_discrete_function_descriptor;
   const std::vector<FunctionSymbolId> m_function_id_list;
 
+  template <size_t Dimension, typename DataType>
+  std::shared_ptr<IDiscreteFunction> _interpolateOnZoneList() const;
+
+  template <size_t Dimension, typename DataType>
+  std::shared_ptr<IDiscreteFunction> _interpolateGlobally() const;
+
   template <size_t Dimension, typename DataType>
   std::shared_ptr<IDiscreteFunction> _interpolate() const;
 
@@ -32,6 +40,17 @@ class DiscreteFunctionVectorInterpoler
     : m_mesh{mesh}, m_discrete_function_descriptor{discrete_function_descriptor}, m_function_id_list{function_id_list}
   {}
 
+  DiscreteFunctionVectorInterpoler(
+    const std::shared_ptr<const IMesh>& mesh,
+    const std::vector<std::shared_ptr<const IZoneDescriptor>>& zone_list,
+    const std::shared_ptr<const IDiscreteFunctionDescriptor>& discrete_function_descriptor,
+    const std::vector<FunctionSymbolId>& function_id_list)
+    : m_mesh{mesh},
+      m_zone_list{zone_list},
+      m_discrete_function_descriptor{discrete_function_descriptor},
+      m_function_id_list{function_id_list}
+  {}
+
   DiscreteFunctionVectorInterpoler(const DiscreteFunctionVectorInterpoler&) = delete;
   DiscreteFunctionVectorInterpoler(DiscreteFunctionVectorInterpoler&&)      = delete;
 
diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt
index 37a87d841e2ad88946edcdfe46abb3fe8ca4ea71..78997684c07a6ffb5457207c6ab4ffaf9d1992f5 100644
--- a/tests/CMakeLists.txt
+++ b/tests/CMakeLists.txt
@@ -158,9 +158,11 @@ add_executable (mpi_unit_tests
   mpi_test_main.cpp
   test_Connectivity.cpp
   test_DiscreteFunctionInterpoler.cpp
+  test_DiscreteFunctionInterpolerByZone.cpp
   test_DiscreteFunctionP0.cpp
   test_DiscreteFunctionP0Vector.cpp
   test_DiscreteFunctionVectorInterpoler.cpp
+  test_DiscreteFunctionVectorInterpolerByZone.cpp
   test_EmbeddedIDiscreteFunctionMathFunctions.cpp
   test_EmbeddedIDiscreteFunctionOperators.cpp
   test_InterpolateItemArray.cpp
diff --git a/tests/test_DiscreteFunctionInterpolerByZone.cpp b/tests/test_DiscreteFunctionInterpolerByZone.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..4ad5f464f5fe276bf489df459cd2cfc90e42a519
--- /dev/null
+++ b/tests/test_DiscreteFunctionInterpolerByZone.cpp
@@ -0,0 +1,1074 @@
+#include <catch2/catch_test_macros.hpp>
+#include <catch2/matchers/catch_matchers_all.hpp>
+
+#include <language/ast/ASTBuilder.hpp>
+#include <language/ast/ASTModulesImporter.hpp>
+#include <language/ast/ASTNodeDataTypeBuilder.hpp>
+#include <language/ast/ASTNodeExpressionBuilder.hpp>
+#include <language/ast/ASTNodeFunctionEvaluationExpressionBuilder.hpp>
+#include <language/ast/ASTNodeFunctionExpressionBuilder.hpp>
+#include <language/ast/ASTNodeTypeCleaner.hpp>
+#include <language/ast/ASTSymbolTableBuilder.hpp>
+#include <language/utils/PugsFunctionAdapter.hpp>
+#include <language/utils/SymbolTable.hpp>
+
+#include <MeshDataBaseForTests.hpp>
+#include <mesh/Connectivity.hpp>
+#include <mesh/Mesh.hpp>
+#include <mesh/MeshCellZone.hpp>
+#include <mesh/MeshData.hpp>
+#include <mesh/MeshDataManager.hpp>
+#include <mesh/NamedZoneDescriptor.hpp>
+
+#include <scheme/DiscreteFunctionDescriptorP0.hpp>
+#include <scheme/DiscreteFunctionInterpoler.hpp>
+#include <scheme/DiscreteFunctionP0.hpp>
+
+#include <pegtl/string_input.hpp>
+
+// clazy:excludeall=non-pod-global-static
+
+TEST_CASE("DiscreteFunctionInterpolerByZone", "[scheme]")
+{
+  auto same_cell_value = [](auto f, auto g) -> bool {
+    using ItemIdType = typename decltype(f)::index_type;
+    for (ItemIdType item_id = 0; item_id < f.numberOfItems(); ++item_id) {
+      if (f[item_id] != g[item_id]) {
+        return false;
+      }
+    }
+
+    return true;
+  };
+
+  SECTION("1D")
+  {
+    constexpr size_t Dimension = 1;
+
+    auto mesh_1d = MeshDataBaseForTests::get().unordered1DMesh();
+
+    std::vector<std::shared_ptr<const IZoneDescriptor>> zone_list;
+    zone_list.push_back(std::make_shared<NamedZoneDescriptor>("LEFT"));
+
+    auto mesh_cell_zone = getMeshCellZone(*mesh_1d, *zone_list[0]);
+    CellValue<bool> is_cell_in_zone{mesh_1d->connectivity()};
+    is_cell_in_zone.fill(false);
+    auto zone_cell_list = mesh_cell_zone.cellList();
+    for (size_t i_cell = 0; i_cell < zone_cell_list.size(); ++i_cell) {
+      is_cell_in_zone[zone_cell_list[i_cell]] = true;
+    }
+
+    auto xj = MeshDataManager::instance().getMeshData(*mesh_1d).xj();
+
+    std::string_view data = R"(
+import math;
+let B_scalar_non_linear_1d: R^1 -> B, x -> (exp(2 * x[0]) + 3 < 3.3);
+let N_scalar_non_linear_1d: R^1 -> N, x -> floor(3 * x[0] * x[0] + 2);
+let Z_scalar_non_linear_1d: R^1 -> Z, x -> floor(exp(2 * x[0]) - 1);
+let R_scalar_non_linear_1d: R^1 -> R, x -> 2 * exp(x[0]) + 3;
+let R1_non_linear_1d: R^1 -> R^1, x -> 2 * exp(x[0]);
+let R2_non_linear_1d: R^1 -> R^2, x -> (2 * exp(x[0]), -3*x[0]);
+let R3_non_linear_1d: R^1 -> R^3, x -> (2 * exp(x[0]) + 3, x[0] - 2, 3);
+let R1x1_non_linear_1d: R^1 -> R^1x1, x -> (2 * exp(x[0]) * sin(x[0]) + 3);
+let R2x2_non_linear_1d: R^1 -> R^2x2, x -> (2 * exp(x[0]) * sin(x[0]) + 3, sin(x[0] - 2 * x[0]), 3, x[0] * x[0]);
+let R3x3_non_linear_1d: R^1 -> R^3x3, x -> (2 * exp(x[0]) * sin(x[0]) + 3, sin(x[0] - 2 * x[0]), 3, x[0] * x[0], -4*x[0], 2*x[0]+1, 3, -6*x[0], exp(x[0]));
+)";
+    TAO_PEGTL_NAMESPACE::string_input input{data, "test.pgs"};
+
+    auto ast = ASTBuilder::build(input);
+
+    ASTModulesImporter{*ast};
+    ASTNodeTypeCleaner<language::import_instruction>{*ast};
+
+    ASTSymbolTableBuilder{*ast};
+    ASTNodeDataTypeBuilder{*ast};
+
+    ASTNodeTypeCleaner<language::var_declaration>{*ast};
+    ASTNodeTypeCleaner<language::fct_declaration>{*ast};
+    ASTNodeExpressionBuilder{*ast};
+
+    std::shared_ptr<SymbolTable> symbol_table = ast->m_symbol_table;
+
+    TAO_PEGTL_NAMESPACE::position position{TAO_PEGTL_NAMESPACE::internal::iterator{"fixture"}, "fixture"};
+    position.byte = data.size();   // ensure that variables are declared at this point
+
+    SECTION("B_scalar_non_linear_1d")
+    {
+      auto [i_symbol, found] = symbol_table->find("B_scalar_non_linear_1d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<double> cell_value{mesh_1d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = std::exp(2 * x[0]) + 3 < 3.3;
+          } else {
+            cell_value[cell_id] = false;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_1d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, double>&>(*discrete_function)));
+    }
+
+    SECTION("N_scalar_non_linear_1d")
+    {
+      auto [i_symbol, found] = symbol_table->find("N_scalar_non_linear_1d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<double> cell_value{mesh_1d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = std::floor(3 * x[0] * x[0] + 2);
+          } else {
+            cell_value[cell_id] = 0;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_1d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, double>&>(*discrete_function)));
+    }
+
+    SECTION("Z_scalar_non_linear_1d")
+    {
+      auto [i_symbol, found] = symbol_table->find("Z_scalar_non_linear_1d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<double> cell_value{mesh_1d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = std::floor(std::exp(2 * x[0]) - 1);
+          } else {
+            cell_value[cell_id] = 0;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_1d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, double>&>(*discrete_function)));
+    }
+
+    SECTION("R_scalar_non_linear_1d")
+    {
+      auto [i_symbol, found] = symbol_table->find("R_scalar_non_linear_1d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<double> cell_value{mesh_1d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = 2 * std::exp(x[0]) + 3;
+          } else {
+            cell_value[cell_id] = 0;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_1d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, double>&>(*discrete_function)));
+    }
+
+    SECTION("R1_non_linear_1d")
+    {
+      using DataType = TinyVector<1>;
+
+      auto [i_symbol, found] = symbol_table->find("R1_non_linear_1d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<DataType> cell_value{mesh_1d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = DataType{2 * std::exp(x[0])};
+          } else {
+            cell_value[cell_id] = zero;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_1d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, DataType>&>(*discrete_function)));
+    }
+
+    SECTION("R2_non_linear_1d")
+    {
+      using DataType = TinyVector<2>;
+
+      auto [i_symbol, found] = symbol_table->find("R2_non_linear_1d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<DataType> cell_value{mesh_1d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = DataType{2 * std::exp(x[0]), -3 * x[0]};
+          } else {
+            cell_value[cell_id] = zero;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_1d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, DataType>&>(*discrete_function)));
+    }
+
+    SECTION("R3_non_linear_1d")
+    {
+      using DataType = TinyVector<3>;
+
+      auto [i_symbol, found] = symbol_table->find("R3_non_linear_1d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<DataType> cell_value{mesh_1d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = DataType{2 * std::exp(x[0]) + 3, x[0] - 2, 3};
+          } else {
+            cell_value[cell_id] = zero;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_1d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, DataType>&>(*discrete_function)));
+    }
+
+    SECTION("R1x1_non_linear_1d")
+    {
+      using DataType = TinyMatrix<1>;
+
+      auto [i_symbol, found] = symbol_table->find("R1x1_non_linear_1d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<DataType> cell_value{mesh_1d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = DataType{2 * std::exp(x[0]) * std::sin(x[0]) + 3};
+          } else {
+            cell_value[cell_id] = zero;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_1d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, DataType>&>(*discrete_function)));
+    }
+
+    SECTION("R2x2_non_linear_1d")
+    {
+      using DataType = TinyMatrix<2>;
+
+      auto [i_symbol, found] = symbol_table->find("R2x2_non_linear_1d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<DataType> cell_value{mesh_1d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id] =
+              DataType{2 * std::exp(x[0]) * std::sin(x[0]) + 3, std::sin(x[0] - 2 * x[0]), 3, x[0] * x[0]};
+          } else {
+            cell_value[cell_id] = zero;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_1d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, DataType>&>(*discrete_function)));
+    }
+
+    SECTION("R3x3_non_linear_1d")
+    {
+      using DataType = TinyMatrix<3>;
+
+      auto [i_symbol, found] = symbol_table->find("R3x3_non_linear_1d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<DataType> cell_value{mesh_1d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = DataType{2 * exp(x[0]) * std::sin(x[0]) + 3,
+                                           std::sin(x[0] - 2 * x[0]),
+                                           3,
+                                           x[0] * x[0],
+                                           -4 * x[0],
+                                           2 * x[0] + 1,
+                                           3,
+                                           -6 * x[0],
+                                           std::exp(x[0])};
+          } else {
+            cell_value[cell_id] = zero;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_1d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, DataType>&>(*discrete_function)));
+    }
+  }
+
+  SECTION("2D")
+  {
+    constexpr size_t Dimension = 2;
+
+    auto mesh_2d = MeshDataBaseForTests::get().hybrid2DMesh();
+
+    std::vector<std::shared_ptr<const IZoneDescriptor>> zone_list;
+    zone_list.push_back(std::make_shared<NamedZoneDescriptor>("LEFT"));
+
+    auto mesh_cell_zone = getMeshCellZone(*mesh_2d, *zone_list[0]);
+    CellValue<bool> is_cell_in_zone{mesh_2d->connectivity()};
+    is_cell_in_zone.fill(false);
+    auto zone_cell_list = mesh_cell_zone.cellList();
+    for (size_t i_cell = 0; i_cell < zone_cell_list.size(); ++i_cell) {
+      is_cell_in_zone[zone_cell_list[i_cell]] = true;
+    }
+
+    auto xj = MeshDataManager::instance().getMeshData(*mesh_2d).xj();
+
+    std::string_view data = R"(
+import math;
+let B_scalar_non_linear_2d: R^2 -> B, x -> (exp(2 * x[0])< 2*x[1]);
+let N_scalar_non_linear_2d: R^2 -> N, x -> floor(3 * (x[0] + x[1]) * (x[0] + x[1]) + 2);
+let Z_scalar_non_linear_2d: R^2 -> Z, x -> floor(exp(2 * x[0]) - 3 * x[1]);
+let R_scalar_non_linear_2d: R^2 -> R, x -> 2 * exp(x[0]) + 3 * x[1];
+let R1_non_linear_2d: R^2 -> R^1, x -> 2 * exp(x[0]);
+let R2_non_linear_2d: R^2 -> R^2, x -> (2 * exp(x[0]), -3*x[1]);
+let R3_non_linear_2d: R^2 -> R^3, x -> (2 * exp(x[0]) + 3, x[1] - 2, 3);
+let R1x1_non_linear_2d: R^2 -> R^1x1, x -> (2 * exp(x[0]) * sin(x[1]) + 3);
+let R2x2_non_linear_2d: R^2 -> R^2x2, x -> (2 * exp(x[0]) * sin(x[1]) + 3, sin(x[1] - 2 * x[0]), 3, x[1] * x[0]);
+let R3x3_non_linear_2d: R^2 -> R^3x3, x -> (2 * exp(x[0]) * sin(x[1]) + 3, sin(x[1] - 2 * x[0]), 3, x[1] * x[0], -4*x[1], 2*x[0]+1, 3, -6*x[0], exp(x[1]));
+)";
+    TAO_PEGTL_NAMESPACE::string_input input{data, "test.pgs"};
+
+    auto ast = ASTBuilder::build(input);
+
+    ASTModulesImporter{*ast};
+    ASTNodeTypeCleaner<language::import_instruction>{*ast};
+
+    ASTSymbolTableBuilder{*ast};
+    ASTNodeDataTypeBuilder{*ast};
+
+    ASTNodeTypeCleaner<language::var_declaration>{*ast};
+    ASTNodeTypeCleaner<language::fct_declaration>{*ast};
+    ASTNodeExpressionBuilder{*ast};
+
+    std::shared_ptr<SymbolTable> symbol_table = ast->m_symbol_table;
+
+    TAO_PEGTL_NAMESPACE::position position{TAO_PEGTL_NAMESPACE::internal::iterator{"fixture"}, "fixture"};
+    position.byte = data.size();   // ensure that variables are declared at this point
+
+    SECTION("B_scalar_non_linear_2d")
+    {
+      auto [i_symbol, found] = symbol_table->find("B_scalar_non_linear_2d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<double> cell_value{mesh_2d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = std::exp(2 * x[0]) < 2 * x[1];
+          } else {
+            cell_value[cell_id] = false;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_2d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, double>&>(*discrete_function)));
+    }
+
+    SECTION("N_scalar_non_linear_2d")
+    {
+      auto [i_symbol, found] = symbol_table->find("N_scalar_non_linear_2d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<double> cell_value{mesh_2d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = std::floor(3 * (x[0] + x[1]) * (x[0] + x[1]) + 2);
+          } else {
+            cell_value[cell_id] = 0;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_2d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, double>&>(*discrete_function)));
+    }
+
+    SECTION("Z_scalar_non_linear_2d")
+    {
+      auto [i_symbol, found] = symbol_table->find("Z_scalar_non_linear_2d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<double> cell_value{mesh_2d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = std::floor(std::exp(2 * x[0]) - 3 * x[1]);
+          } else {
+            cell_value[cell_id] = 0;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_2d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, double>&>(*discrete_function)));
+    }
+
+    SECTION("R_scalar_non_linear_2d")
+    {
+      auto [i_symbol, found] = symbol_table->find("R_scalar_non_linear_2d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<double> cell_value{mesh_2d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = 2 * std::exp(x[0]) + 3 * x[1];
+          } else {
+            cell_value[cell_id] = 0;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_2d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, double>&>(*discrete_function)));
+    }
+
+    SECTION("R1_non_linear_2d")
+    {
+      using DataType = TinyVector<1>;
+
+      auto [i_symbol, found] = symbol_table->find("R1_non_linear_2d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<DataType> cell_value{mesh_2d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = DataType{2 * std::exp(x[0])};
+          } else {
+            cell_value[cell_id] = zero;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_2d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, DataType>&>(*discrete_function)));
+    }
+
+    SECTION("R2_non_linear_2d")
+    {
+      using DataType = TinyVector<2>;
+
+      auto [i_symbol, found] = symbol_table->find("R2_non_linear_2d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<DataType> cell_value{mesh_2d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = DataType{2 * std::exp(x[0]), -3 * x[1]};
+          } else {
+            cell_value[cell_id] = zero;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_2d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, DataType>&>(*discrete_function)));
+    }
+
+    SECTION("R3_non_linear_2d")
+    {
+      using DataType = TinyVector<3>;
+
+      auto [i_symbol, found] = symbol_table->find("R3_non_linear_2d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<DataType> cell_value{mesh_2d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = DataType{2 * std::exp(x[0]) + 3, x[1] - 2, 3};
+          } else {
+            cell_value[cell_id] = zero;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_2d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, DataType>&>(*discrete_function)));
+    }
+
+    SECTION("R1x1_non_linear_2d")
+    {
+      using DataType = TinyMatrix<1>;
+
+      auto [i_symbol, found] = symbol_table->find("R1x1_non_linear_2d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<DataType> cell_value{mesh_2d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = DataType{2 * std::exp(x[0]) * std::sin(x[1]) + 3};
+          } else {
+            cell_value[cell_id] = zero;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_2d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, DataType>&>(*discrete_function)));
+    }
+
+    SECTION("R2x2_non_linear_2d")
+    {
+      using DataType = TinyMatrix<2>;
+
+      auto [i_symbol, found] = symbol_table->find("R2x2_non_linear_2d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<DataType> cell_value{mesh_2d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id] =
+              DataType{2 * std::exp(x[0]) * std::sin(x[1]) + 3, std::sin(x[1] - 2 * x[0]), 3, x[1] * x[0]};
+          } else {
+            cell_value[cell_id] = zero;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_2d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, DataType>&>(*discrete_function)));
+    }
+
+    SECTION("R3x3_non_linear_2d")
+    {
+      using DataType = TinyMatrix<3>;
+
+      auto [i_symbol, found] = symbol_table->find("R3x3_non_linear_2d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<DataType> cell_value{mesh_2d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+
+            cell_value[cell_id] = DataType{2 * std::exp(x[0]) * std::sin(x[1]) + 3,
+                                           std::sin(x[1] - 2 * x[0]),
+                                           3,
+                                           x[1] * x[0],
+                                           -4 * x[1],
+                                           2 * x[0] + 1,
+                                           3,
+                                           -6 * x[0],
+                                           std::exp(x[1])};
+          } else {
+            cell_value[cell_id] = zero;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_2d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, DataType>&>(*discrete_function)));
+    }
+  }
+
+  SECTION("3D")
+  {
+    constexpr size_t Dimension = 3;
+
+    auto mesh_3d = MeshDataBaseForTests::get().hybrid3DMesh();
+
+    std::vector<std::shared_ptr<const IZoneDescriptor>> zone_list;
+    zone_list.push_back(std::make_shared<NamedZoneDescriptor>("LEFT"));
+
+    auto mesh_cell_zone = getMeshCellZone(*mesh_3d, *zone_list[0]);
+    CellValue<bool> is_cell_in_zone{mesh_3d->connectivity()};
+    is_cell_in_zone.fill(false);
+    auto zone_cell_list = mesh_cell_zone.cellList();
+    for (size_t i_cell = 0; i_cell < zone_cell_list.size(); ++i_cell) {
+      is_cell_in_zone[zone_cell_list[i_cell]] = true;
+    }
+
+    auto xj = MeshDataManager::instance().getMeshData(*mesh_3d).xj();
+
+    std::string_view data = R"(
+import math;
+let B_scalar_non_linear_3d: R^3 -> B, x -> (exp(2 * x[0])< 2*x[1]+x[2]);
+let N_scalar_non_linear_3d: R^3 -> N, x -> floor(3 * (x[0] + x[1]) * (x[0] + x[1]) + x[2] * x[2]);
+let Z_scalar_non_linear_3d: R^3 -> Z, x -> floor(exp(2 * x[0]) - 3 * x[1] + x[2]);
+let R_scalar_non_linear_3d: R^3 -> R, x -> 2 * exp(x[0]+x[2]) + 3 * x[1];
+let R1_non_linear_3d: R^3 -> R^1, x -> 2 * exp(x[0])+sin(x[1] + x[2]);
+let R2_non_linear_3d: R^3 -> R^2, x -> (2 * exp(x[0]), -3*x[1] * x[2]);
+let R3_non_linear_3d: R^3 -> R^3, x -> (2 * exp(x[0]) + 3, x[1] - 2, 3 * x[2]);
+let R1x1_non_linear_3d: R^3 -> R^1x1, x -> (2 * exp(x[0]) * sin(x[1]) + 3 * x[2]);
+let R2x2_non_linear_3d: R^3 -> R^2x2, x -> (2 * exp(x[0]) * sin(x[1]) + 3, sin(x[2] - 2 * x[0]), 3, x[1] * x[0] - x[2]);
+let R3x3_non_linear_3d: R^3 -> R^3x3, x -> (2 * exp(x[0]) * sin(x[1]) + 3, sin(x[1] - 2 * x[2]), 3, x[1] * x[2], -4*x[1], 2*x[2]+1, 3, -6*x[2], exp(x[1] + x[2]));
+)";
+    TAO_PEGTL_NAMESPACE::string_input input{data, "test.pgs"};
+
+    auto ast = ASTBuilder::build(input);
+
+    ASTModulesImporter{*ast};
+    ASTNodeTypeCleaner<language::import_instruction>{*ast};
+
+    ASTSymbolTableBuilder{*ast};
+    ASTNodeDataTypeBuilder{*ast};
+
+    ASTNodeTypeCleaner<language::var_declaration>{*ast};
+    ASTNodeTypeCleaner<language::fct_declaration>{*ast};
+    ASTNodeExpressionBuilder{*ast};
+
+    std::shared_ptr<SymbolTable> symbol_table = ast->m_symbol_table;
+
+    TAO_PEGTL_NAMESPACE::position position{TAO_PEGTL_NAMESPACE::internal::iterator{"fixture"}, "fixture"};
+    position.byte = data.size();   // ensure that variables are declared at this point
+
+    SECTION("B_scalar_non_linear_3d")
+    {
+      auto [i_symbol, found] = symbol_table->find("B_scalar_non_linear_3d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<double> cell_value{mesh_3d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = std::exp(2 * x[0]) < 2 * x[1] + x[2];
+          } else {
+            cell_value[cell_id] = false;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_3d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, double>&>(*discrete_function)));
+    }
+
+    SECTION("N_scalar_non_linear_3d")
+    {
+      auto [i_symbol, found] = symbol_table->find("N_scalar_non_linear_3d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<double> cell_value{mesh_3d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = std::floor(3 * (x[0] + x[1]) * (x[0] + x[1]) + x[2] * x[2]);
+          } else {
+            cell_value[cell_id] = 0;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_3d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, double>&>(*discrete_function)));
+    }
+
+    SECTION("Z_scalar_non_linear_3d")
+    {
+      auto [i_symbol, found] = symbol_table->find("Z_scalar_non_linear_3d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<double> cell_value{mesh_3d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = std::floor(std::exp(2 * x[0]) - 3 * x[1] + x[2]);
+          } else {
+            cell_value[cell_id] = 0;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_3d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, double>&>(*discrete_function)));
+    }
+
+    SECTION("R_scalar_non_linear_3d")
+    {
+      auto [i_symbol, found] = symbol_table->find("R_scalar_non_linear_3d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<double> cell_value{mesh_3d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = 2 * std::exp(x[0] + x[2]) + 3 * x[1];
+          } else {
+            cell_value[cell_id] = 0;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_3d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, double>&>(*discrete_function)));
+    }
+
+    SECTION("R1_non_linear_3d")
+    {
+      using DataType = TinyVector<1>;
+
+      auto [i_symbol, found] = symbol_table->find("R1_non_linear_3d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<DataType> cell_value{mesh_3d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = DataType{2 * std::exp(x[0]) + std::sin(x[1] + x[2])};
+          } else {
+            cell_value[cell_id] = zero;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_3d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, DataType>&>(*discrete_function)));
+    }
+
+    SECTION("R2_non_linear_3d")
+    {
+      using DataType = TinyVector<2>;
+
+      auto [i_symbol, found] = symbol_table->find("R2_non_linear_3d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<DataType> cell_value{mesh_3d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = DataType{2 * std::exp(x[0]), -3 * x[1] * x[2]};
+          } else {
+            cell_value[cell_id] = zero;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_3d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, DataType>&>(*discrete_function)));
+    }
+
+    SECTION("R3_non_linear_3d")
+    {
+      using DataType = TinyVector<3>;
+
+      auto [i_symbol, found] = symbol_table->find("R3_non_linear_3d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<DataType> cell_value{mesh_3d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = DataType{2 * std::exp(x[0]) + 3, x[1] - 2, 3 * x[2]};
+          } else {
+            cell_value[cell_id] = zero;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_3d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, DataType>&>(*discrete_function)));
+    }
+
+    SECTION("R1x1_non_linear_3d")
+    {
+      using DataType = TinyMatrix<1>;
+
+      auto [i_symbol, found] = symbol_table->find("R1x1_non_linear_3d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<DataType> cell_value{mesh_3d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = DataType{2 * std::exp(x[0]) * std::sin(x[1]) + 3 * x[2]};
+          } else {
+            cell_value[cell_id] = zero;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_3d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, DataType>&>(*discrete_function)));
+    }
+
+    SECTION("R2x2_non_linear_3d")
+    {
+      using DataType = TinyMatrix<2>;
+
+      auto [i_symbol, found] = symbol_table->find("R2x2_non_linear_3d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<DataType> cell_value{mesh_3d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id] =
+              DataType{2 * std::exp(x[0]) * std::sin(x[1]) + 3, std::sin(x[2] - 2 * x[0]), 3, x[1] * x[0] - x[2]};
+          } else {
+            cell_value[cell_id] = zero;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_3d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, DataType>&>(*discrete_function)));
+    }
+
+    SECTION("R3x3_non_linear_3d")
+    {
+      using DataType = TinyMatrix<3>;
+
+      auto [i_symbol, found] = symbol_table->find("R3x3_non_linear_3d", position);
+      REQUIRE(found);
+      REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+      FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+
+      CellValue<DataType> cell_value{mesh_3d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+
+            cell_value[cell_id] = DataType{2 * std::exp(x[0]) * std::sin(x[1]) + 3,
+                                           std::sin(x[1] - 2 * x[2]),
+                                           3,
+                                           x[1] * x[2],
+                                           -4 * x[1],
+                                           2 * x[2] + 1,
+                                           3,
+                                           -6 * x[2],
+                                           std::exp(x[1] + x[2])};
+          } else {
+            cell_value[cell_id] = zero;
+          }
+        });
+
+      DiscreteFunctionInterpoler interpoler(mesh_3d, zone_list, std::make_shared<DiscreteFunctionDescriptorP0>(),
+                                            function_symbol_id);
+      std::shared_ptr discrete_function = interpoler.interpolate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, DataType>&>(*discrete_function)));
+    }
+  }
+}
diff --git a/tests/test_DiscreteFunctionVectorInterpolerByZone.cpp b/tests/test_DiscreteFunctionVectorInterpolerByZone.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..172c68d4f59f318d0f36c315aaf4962e71195dbe
--- /dev/null
+++ b/tests/test_DiscreteFunctionVectorInterpolerByZone.cpp
@@ -0,0 +1,511 @@
+#include <catch2/catch_test_macros.hpp>
+#include <catch2/matchers/catch_matchers_all.hpp>
+
+#include <language/ast/ASTBuilder.hpp>
+#include <language/ast/ASTModulesImporter.hpp>
+#include <language/ast/ASTNodeDataTypeBuilder.hpp>
+#include <language/ast/ASTNodeExpressionBuilder.hpp>
+#include <language/ast/ASTNodeFunctionEvaluationExpressionBuilder.hpp>
+#include <language/ast/ASTNodeFunctionExpressionBuilder.hpp>
+#include <language/ast/ASTNodeTypeCleaner.hpp>
+#include <language/ast/ASTSymbolTableBuilder.hpp>
+#include <language/utils/PugsFunctionAdapter.hpp>
+#include <language/utils/SymbolTable.hpp>
+
+#include <MeshDataBaseForTests.hpp>
+#include <mesh/Connectivity.hpp>
+#include <mesh/Mesh.hpp>
+#include <mesh/MeshCellZone.hpp>
+#include <mesh/MeshData.hpp>
+#include <mesh/MeshDataManager.hpp>
+#include <mesh/NamedZoneDescriptor.hpp>
+
+#include <scheme/DiscreteFunctionDescriptorP0Vector.hpp>
+#include <scheme/DiscreteFunctionP0Vector.hpp>
+#include <scheme/DiscreteFunctionVectorInterpoler.hpp>
+
+#include <pegtl/string_input.hpp>
+
+// clazy:excludeall=non-pod-global-static
+
+TEST_CASE("DiscreteFunctionVectorInterpolerByZone", "[scheme]")
+{
+  auto same_cell_value = [](const CellValue<const double>& fi, const size_t i, const auto& f) -> bool {
+    for (CellId cell_id = 0; cell_id < fi.numberOfItems(); ++cell_id) {
+      if (fi[cell_id] != f[cell_id][i]) {
+        return false;
+      }
+    }
+
+    return true;
+  };
+
+  auto register_function = [](const TAO_PEGTL_NAMESPACE::position& position,
+                              const std::shared_ptr<SymbolTable>& symbol_table, const std::string& name,
+                              std::vector<FunctionSymbolId>& function_id_list) {
+    auto [i_symbol, found] = symbol_table->find(name, position);
+    REQUIRE(found);
+    REQUIRE(i_symbol->attributes().dataType() == ASTNodeDataType::function_t);
+
+    FunctionSymbolId function_symbol_id(std::get<uint64_t>(i_symbol->attributes().value()), symbol_table);
+    function_id_list.push_back(function_symbol_id);
+  };
+
+  SECTION("1D")
+  {
+    constexpr size_t Dimension = 1;
+
+    auto mesh_1d = MeshDataBaseForTests::get().unordered1DMesh();
+
+    std::vector<std::shared_ptr<const IZoneDescriptor>> zone_list;
+    zone_list.push_back(std::make_shared<NamedZoneDescriptor>("LEFT"));
+
+    auto mesh_cell_zone = getMeshCellZone(*mesh_1d, *zone_list[0]);
+    CellValue<bool> is_cell_in_zone{mesh_1d->connectivity()};
+    is_cell_in_zone.fill(false);
+    auto zone_cell_list = mesh_cell_zone.cellList();
+    for (size_t i_cell = 0; i_cell < zone_cell_list.size(); ++i_cell) {
+      is_cell_in_zone[zone_cell_list[i_cell]] = true;
+    }
+
+    auto xj = MeshDataManager::instance().getMeshData(*mesh_1d).xj();
+
+    std::string_view data = R"(
+import math;
+let B_scalar_non_linear_1d: R^1 -> B, x -> (exp(2 * x[0]) + 3 > 4);
+let N_scalar_non_linear_1d: R^1 -> N, x -> floor(3 * x[0] * x[0] + 2);
+let Z_scalar_non_linear_1d: R^1 -> Z, x -> floor(exp(2 * x[0]) - 1);
+let R_scalar_non_linear_1d: R^1 -> R, x -> 2 * exp(x[0]) + 3;
+)";
+    TAO_PEGTL_NAMESPACE::string_input input{data, "test.pgs"};
+
+    auto ast = ASTBuilder::build(input);
+
+    ASTModulesImporter{*ast};
+    ASTNodeTypeCleaner<language::import_instruction>{*ast};
+
+    ASTSymbolTableBuilder{*ast};
+    ASTNodeDataTypeBuilder{*ast};
+
+    ASTNodeTypeCleaner<language::var_declaration>{*ast};
+    ASTNodeTypeCleaner<language::fct_declaration>{*ast};
+    ASTNodeExpressionBuilder{*ast};
+
+    TAO_PEGTL_NAMESPACE::position position{TAO_PEGTL_NAMESPACE::internal::iterator{"fixture"}, "fixture"};
+    position.byte = data.size();   // ensure that variables are declared at this point
+
+    std::shared_ptr<SymbolTable> symbol_table = ast->m_symbol_table;
+
+    std::vector<FunctionSymbolId> function_id_list;
+    register_function(position, symbol_table, "B_scalar_non_linear_1d", function_id_list);
+    register_function(position, symbol_table, "N_scalar_non_linear_1d", function_id_list);
+    register_function(position, symbol_table, "Z_scalar_non_linear_1d", function_id_list);
+    register_function(position, symbol_table, "R_scalar_non_linear_1d", function_id_list);
+
+    DiscreteFunctionVectorInterpoler interpoler(mesh_1d, zone_list,
+                                                std::make_shared<DiscreteFunctionDescriptorP0Vector>(),
+                                                function_id_list);
+    std::shared_ptr discrete_function = interpoler.interpolate();
+
+    size_t i = 0;
+
+    {
+      CellValue<double> cell_value{mesh_1d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = std::exp(2 * x[0]) + 3 > 4;
+          } else {
+            cell_value[cell_id] = 0;
+          }
+        });
+
+      REQUIRE(same_cell_value(cell_value, i++,
+                              dynamic_cast<const DiscreteFunctionP0Vector<Dimension, double>&>(*discrete_function)));
+    }
+
+    {
+      CellValue<double> cell_value{mesh_1d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = std::floor(3 * x[0] * x[0] + 2);
+          } else {
+            cell_value[cell_id] = 0;
+          }
+        });
+
+      REQUIRE(same_cell_value(cell_value, i++,
+                              dynamic_cast<const DiscreteFunctionP0Vector<Dimension, double>&>(*discrete_function)));
+    }
+
+    {
+      CellValue<double> cell_value{mesh_1d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = std::floor(std::exp(2 * x[0]) - 1);
+          } else {
+            cell_value[cell_id] = 0;
+          }
+        });
+
+      REQUIRE(same_cell_value(cell_value, i++,
+                              dynamic_cast<const DiscreteFunctionP0Vector<Dimension, double>&>(*discrete_function)));
+    }
+
+    {
+      CellValue<double> cell_value{mesh_1d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = 2 * std::exp(x[0]) + 3;
+          } else {
+            cell_value[cell_id] = 0;
+          }
+        });
+
+      REQUIRE(same_cell_value(cell_value, i++,
+                              dynamic_cast<const DiscreteFunctionP0Vector<Dimension, double>&>(*discrete_function)));
+    }
+
+    REQUIRE(i == function_id_list.size());
+  }
+
+  SECTION("2D")
+  {
+    constexpr size_t Dimension = 2;
+
+    auto mesh_2d = MeshDataBaseForTests::get().hybrid2DMesh();
+
+    std::vector<std::shared_ptr<const IZoneDescriptor>> zone_list;
+    zone_list.push_back(std::make_shared<NamedZoneDescriptor>("LEFT"));
+
+    auto mesh_cell_zone = getMeshCellZone(*mesh_2d, *zone_list[0]);
+    CellValue<bool> is_cell_in_zone{mesh_2d->connectivity()};
+    is_cell_in_zone.fill(false);
+    auto zone_cell_list = mesh_cell_zone.cellList();
+    for (size_t i_cell = 0; i_cell < zone_cell_list.size(); ++i_cell) {
+      is_cell_in_zone[zone_cell_list[i_cell]] = true;
+    }
+
+    auto xj = MeshDataManager::instance().getMeshData(*mesh_2d).xj();
+
+    std::string_view data = R"(
+import math;
+let B_scalar_non_linear_2d: R^2 -> B, x -> (exp(2 * x[0]) + 3 > 4);
+let N_scalar_non_linear_2d: R^2 -> N, x -> floor(3 * (x[0] * x[1]) * (x[0] * x[1]) + 2);
+let Z_scalar_non_linear_2d: R^2 -> Z, x -> floor(exp(2 * x[1]) - 1);
+let R_scalar_non_linear_2d: R^2 -> R, x -> 2 * exp(x[0] + x[1]) + 3;
+)";
+    TAO_PEGTL_NAMESPACE::string_input input{data, "test.pgs"};
+
+    auto ast = ASTBuilder::build(input);
+
+    ASTModulesImporter{*ast};
+    ASTNodeTypeCleaner<language::import_instruction>{*ast};
+
+    ASTSymbolTableBuilder{*ast};
+    ASTNodeDataTypeBuilder{*ast};
+
+    ASTNodeTypeCleaner<language::var_declaration>{*ast};
+    ASTNodeTypeCleaner<language::fct_declaration>{*ast};
+    ASTNodeExpressionBuilder{*ast};
+
+    TAO_PEGTL_NAMESPACE::position position{TAO_PEGTL_NAMESPACE::internal::iterator{"fixture"}, "fixture"};
+    position.byte = data.size();   // ensure that variables are declared at this point
+
+    std::shared_ptr<SymbolTable> symbol_table = ast->m_symbol_table;
+
+    std::vector<FunctionSymbolId> function_id_list;
+    register_function(position, symbol_table, "B_scalar_non_linear_2d", function_id_list);
+    register_function(position, symbol_table, "N_scalar_non_linear_2d", function_id_list);
+    register_function(position, symbol_table, "Z_scalar_non_linear_2d", function_id_list);
+    register_function(position, symbol_table, "R_scalar_non_linear_2d", function_id_list);
+
+    DiscreteFunctionVectorInterpoler interpoler(mesh_2d, zone_list,
+                                                std::make_shared<DiscreteFunctionDescriptorP0Vector>(),
+                                                function_id_list);
+    std::shared_ptr discrete_function = interpoler.interpolate();
+
+    size_t i = 0;
+
+    {
+      CellValue<double> cell_value{mesh_2d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = std::exp(2 * x[0]) + 3 > 4;
+          } else {
+            cell_value[cell_id] = 0;
+          }
+        });
+
+      REQUIRE(same_cell_value(cell_value, i++,
+                              dynamic_cast<const DiscreteFunctionP0Vector<Dimension, double>&>(*discrete_function)));
+    }
+
+    {
+      CellValue<double> cell_value{mesh_2d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = std::floor(3 * (x[0] * x[1]) * (x[0] * x[1]) + 2);
+          } else {
+            cell_value[cell_id] = 0;
+          }
+        });
+
+      REQUIRE(same_cell_value(cell_value, i++,
+                              dynamic_cast<const DiscreteFunctionP0Vector<Dimension, double>&>(*discrete_function)));
+    }
+
+    {
+      CellValue<double> cell_value{mesh_2d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = std::floor(std::exp(2 * x[1]) - 1);
+          } else {
+            cell_value[cell_id] = 0;
+          }
+        });
+
+      REQUIRE(same_cell_value(cell_value, i++,
+                              dynamic_cast<const DiscreteFunctionP0Vector<Dimension, double>&>(*discrete_function)));
+    }
+
+    {
+      CellValue<double> cell_value{mesh_2d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = 2 * std::exp(x[0] + x[1]) + 3;
+          } else {
+            cell_value[cell_id] = 0;
+          }
+        });
+
+      REQUIRE(same_cell_value(cell_value, i++,
+                              dynamic_cast<const DiscreteFunctionP0Vector<Dimension, double>&>(*discrete_function)));
+    }
+
+    REQUIRE(i == function_id_list.size());
+  }
+
+  SECTION("3D")
+  {
+    constexpr size_t Dimension = 3;
+
+    auto mesh_3d = MeshDataBaseForTests::get().hybrid3DMesh();
+
+    std::vector<std::shared_ptr<const IZoneDescriptor>> zone_list;
+    zone_list.push_back(std::make_shared<NamedZoneDescriptor>("LEFT"));
+
+    auto mesh_cell_zone = getMeshCellZone(*mesh_3d, *zone_list[0]);
+    CellValue<bool> is_cell_in_zone{mesh_3d->connectivity()};
+    is_cell_in_zone.fill(false);
+    auto zone_cell_list = mesh_cell_zone.cellList();
+    for (size_t i_cell = 0; i_cell < zone_cell_list.size(); ++i_cell) {
+      is_cell_in_zone[zone_cell_list[i_cell]] = true;
+    }
+
+    auto xj = MeshDataManager::instance().getMeshData(*mesh_3d).xj();
+
+    std::string_view data = R"(
+import math;
+let B_scalar_non_linear_3d: R^3 -> B, x -> (exp(2 * x[0] + x[2]) + 3 > 4);
+let N_scalar_non_linear_3d: R^3 -> N, x -> floor(3 * (x[0] * x[1]) * (x[0] * x[1]) + 2);
+let Z_scalar_non_linear_3d: R^3 -> Z, x -> floor(exp(2 * x[1]) - x[2]);
+let R_scalar_non_linear_3d: R^3 -> R, x -> 2 * exp(x[0] + x[1]) + 3 * x[2];
+)";
+    TAO_PEGTL_NAMESPACE::string_input input{data, "test.pgs"};
+
+    auto ast = ASTBuilder::build(input);
+
+    ASTModulesImporter{*ast};
+    ASTNodeTypeCleaner<language::import_instruction>{*ast};
+
+    ASTSymbolTableBuilder{*ast};
+    ASTNodeDataTypeBuilder{*ast};
+
+    ASTNodeTypeCleaner<language::var_declaration>{*ast};
+    ASTNodeTypeCleaner<language::fct_declaration>{*ast};
+    ASTNodeExpressionBuilder{*ast};
+
+    TAO_PEGTL_NAMESPACE::position position{TAO_PEGTL_NAMESPACE::internal::iterator{"fixture"}, "fixture"};
+    position.byte = data.size();   // ensure that variables are declared at this point
+
+    std::shared_ptr<SymbolTable> symbol_table = ast->m_symbol_table;
+
+    std::vector<FunctionSymbolId> function_id_list;
+    register_function(position, symbol_table, "B_scalar_non_linear_3d", function_id_list);
+    register_function(position, symbol_table, "N_scalar_non_linear_3d", function_id_list);
+    register_function(position, symbol_table, "Z_scalar_non_linear_3d", function_id_list);
+    register_function(position, symbol_table, "R_scalar_non_linear_3d", function_id_list);
+
+    DiscreteFunctionVectorInterpoler interpoler(mesh_3d, zone_list,
+                                                std::make_shared<DiscreteFunctionDescriptorP0Vector>(),
+                                                function_id_list);
+    std::shared_ptr discrete_function = interpoler.interpolate();
+
+    size_t i = 0;
+
+    {
+      CellValue<double> cell_value{mesh_3d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = std::exp(2 * x[0] + x[2]) + 3 > 4;
+          } else {
+            cell_value[cell_id] = 0;
+          }
+        });
+
+      REQUIRE(same_cell_value(cell_value, i++,
+                              dynamic_cast<const DiscreteFunctionP0Vector<Dimension, double>&>(*discrete_function)));
+    }
+
+    {
+      CellValue<double> cell_value{mesh_3d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = std::floor(3 * (x[0] * x[1]) * (x[0] * x[1]) + 2);
+          } else {
+            cell_value[cell_id] = 0;
+          }
+        });
+
+      REQUIRE(same_cell_value(cell_value, i++,
+                              dynamic_cast<const DiscreteFunctionP0Vector<Dimension, double>&>(*discrete_function)));
+    }
+
+    {
+      CellValue<double> cell_value{mesh_3d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = std::floor(std::exp(2 * x[1]) - x[2]);
+          } else {
+            cell_value[cell_id] = 0;
+          }
+        });
+
+      REQUIRE(same_cell_value(cell_value, i++,
+                              dynamic_cast<const DiscreteFunctionP0Vector<Dimension, double>&>(*discrete_function)));
+    }
+
+    {
+      CellValue<double> cell_value{mesh_3d->connectivity()};
+      parallel_for(
+        cell_value.numberOfItems(), PUGS_LAMBDA(const CellId cell_id) {
+          if (is_cell_in_zone[cell_id]) {
+            const TinyVector<Dimension>& x = xj[cell_id];
+            cell_value[cell_id]            = 2 * std::exp(x[0] + x[1]) + 3 * x[2];
+          } else {
+            cell_value[cell_id] = 0;
+          }
+        });
+
+      REQUIRE(same_cell_value(cell_value, i++,
+                              dynamic_cast<const DiscreteFunctionP0Vector<Dimension, double>&>(*discrete_function)));
+    }
+
+    REQUIRE(i == function_id_list.size());
+  }
+
+  SECTION("errors")
+  {
+    std::array mesh_list = MeshDataBaseForTests::get().all3DMeshes();
+
+    for (auto named_mesh : mesh_list) {
+      SECTION(named_mesh.name())
+      {
+        auto mesh_3d = named_mesh.mesh();
+
+        auto xj = MeshDataManager::instance().getMeshData(*mesh_3d).xj();
+
+        std::string_view data = R"(
+import math;
+let B_scalar_non_linear_2d: R^2 -> B, x -> (exp(2 * x[0] + x[1]) + 3 > 4);
+let N_scalar_non_linear_1d: R^1 -> N, x -> floor(3 * x[0] * x[0] + 2);
+let Z_scalar_non_linear_3d: R^3 -> Z, x -> floor(exp(2 * x[1]) - x[2]);
+let R_scalar_non_linear_3d: R^3 -> R, x -> 2 * exp(x[0] + x[1]) + 3 * x[2];
+let R2_scalar_non_linear_3d: R^3 -> R^2, x -> (2 * exp(x[0] + x[1]) + 3 * x[2], x[0] - x[1]);
+)";
+        TAO_PEGTL_NAMESPACE::string_input input{data, "test.pgs"};
+
+        auto ast = ASTBuilder::build(input);
+
+        ASTModulesImporter{*ast};
+        ASTNodeTypeCleaner<language::import_instruction>{*ast};
+
+        ASTSymbolTableBuilder{*ast};
+        ASTNodeDataTypeBuilder{*ast};
+
+        ASTNodeTypeCleaner<language::var_declaration>{*ast};
+        ASTNodeTypeCleaner<language::fct_declaration>{*ast};
+        ASTNodeExpressionBuilder{*ast};
+
+        TAO_PEGTL_NAMESPACE::position position{TAO_PEGTL_NAMESPACE::internal::iterator{"fixture"}, "fixture"};
+        position.byte = data.size();   // ensure that variables are declared at this point
+
+        std::shared_ptr<SymbolTable> symbol_table = ast->m_symbol_table;
+
+        SECTION("invalid function type")
+        {
+          std::vector<FunctionSymbolId> function_id_list;
+          register_function(position, symbol_table, "B_scalar_non_linear_2d", function_id_list);
+          register_function(position, symbol_table, "N_scalar_non_linear_1d", function_id_list);
+          register_function(position, symbol_table, "Z_scalar_non_linear_3d", function_id_list);
+          register_function(position, symbol_table, "R_scalar_non_linear_3d", function_id_list);
+
+          DiscreteFunctionVectorInterpoler interpoler(mesh_3d, std::make_shared<DiscreteFunctionDescriptorP0Vector>(),
+                                                      function_id_list);
+
+          const std::string error_msg = R"(error: invalid function type
+note: expecting R^3 -> R
+note: provided function B_scalar_non_linear_2d: R^2 -> B)";
+
+          REQUIRE_THROWS_WITH(interpoler.interpolate(), error_msg);
+        }
+
+        SECTION("invalid value type")
+        {
+          std::vector<FunctionSymbolId> function_id_list;
+          register_function(position, symbol_table, "Z_scalar_non_linear_3d", function_id_list);
+          register_function(position, symbol_table, "R_scalar_non_linear_3d", function_id_list);
+          register_function(position, symbol_table, "R2_scalar_non_linear_3d", function_id_list);
+
+          DiscreteFunctionVectorInterpoler interpoler(mesh_3d, std::make_shared<DiscreteFunctionDescriptorP0Vector>(),
+                                                      function_id_list);
+
+          const std::string error_msg = R"(error: vector functions require scalar value type.
+Invalid interpolation value type: R^2)";
+
+          REQUIRE_THROWS_WITH(interpoler.interpolate(), error_msg);
+        }
+
+        SECTION("invalid discrete function type")
+        {
+          const std::string error_msg = "error: invalid discrete function type for vector interpolation";
+
+          DiscreteFunctionVectorInterpoler interpoler{mesh_3d, std::make_shared<DiscreteFunctionDescriptorP0>(), {}};
+          REQUIRE_THROWS_WITH(interpoler.interpolate(), error_msg);
+        }
+      }
+    }
+  }
+}