diff --git a/src/scheme/DiscreteFunctionIntegrator.cpp b/src/scheme/DiscreteFunctionIntegrator.cpp
index c6a950a9ddc7f088996425da48a0affdcf61d233..93c836461ce14ae05b51b879cf90525f73a793eb 100644
--- a/src/scheme/DiscreteFunctionIntegrator.cpp
+++ b/src/scheme/DiscreteFunctionIntegrator.cpp
@@ -46,10 +46,10 @@ DiscreteFunctionIntegrator::_integrateOnZoneList() const
     }
   }
 
-  Array<DataType> array =
-    IntegrateCellValue<DataType(TinyVector<Dimension>)>::template integrate<MeshType>(m_function_id,
-                                                                                      *m_quadrature_descriptor, *p_mesh,
-                                                                                      zone_cell_list);
+  Array<ValueType> array =
+    IntegrateCellValue<ValueType(TinyVector<Dimension>)>::template integrate<MeshType>(m_function_id,
+                                                                                       *m_quadrature_descriptor,
+                                                                                       *p_mesh, zone_cell_list);
 
   CellValue<ValueType> cell_value{p_mesh->connectivity()};
   if constexpr (is_tiny_vector_v<ValueType> or is_tiny_matrix_v<ValueType>) {
diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt
index 2fd2c19e0bc610f8d82cc355ea1965eb486c7b3b..5035890f67986977626aaf13dbae968269aa66b6 100644
--- a/tests/CMakeLists.txt
+++ b/tests/CMakeLists.txt
@@ -158,6 +158,7 @@ add_executable (mpi_unit_tests
   mpi_test_main.cpp
   test_Connectivity.cpp
   test_DiscreteFunctionIntegrator.cpp
+  test_DiscreteFunctionIntegratorByZone.cpp
   test_DiscreteFunctionInterpoler.cpp
   test_DiscreteFunctionInterpolerByZone.cpp
   test_DiscreteFunctionP0.cpp
diff --git a/tests/test_DiscreteFunctionIntegratorByZone.cpp b/tests/test_DiscreteFunctionIntegratorByZone.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..071f8cddb7e9f71e0b102bf361afb8715a7afe87
--- /dev/null
+++ b/tests/test_DiscreteFunctionIntegratorByZone.cpp
@@ -0,0 +1,1062 @@
+#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 <analysis/GaussQuadratureDescriptor.hpp>
+#include <language/utils/IntegrateCellValue.hpp>
+#include <scheme/DiscreteFunctionDescriptorP0.hpp>
+#include <scheme/DiscreteFunctionIntegrator.hpp>
+#include <scheme/DiscreteFunctionP0.hpp>
+
+#include <pegtl/string_input.hpp>
+
+// clazy:excludeall=non-pod-global-static
+
+TEST_CASE("DiscreteFunctionIntegratorByZone", "[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;
+
+    std::shared_ptr<const IQuadratureDescriptor> quadrature_descriptor = std::make_shared<GaussQuadratureDescriptor>(3);
+
+    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]);
+    auto zone_cell_list = mesh_cell_zone.cellList();
+
+    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);
+
+      Array<double> array =
+        IntegrateCellValue<double(TinyVector<1>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_1d,
+                                                             zone_cell_list);
+
+      CellValue<double> cell_value{mesh_1d->connectivity()};
+      cell_value.fill(0);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_1d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<double> array =
+        IntegrateCellValue<double(TinyVector<1>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_1d,
+                                                             zone_cell_list);
+
+      CellValue<double> cell_value{mesh_1d->connectivity()};
+      cell_value.fill(0);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_1d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<double> array =
+        IntegrateCellValue<double(TinyVector<1>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_1d,
+                                                             zone_cell_list);
+
+      CellValue<double> cell_value{mesh_1d->connectivity()};
+      cell_value.fill(0);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_1d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<double> array =
+        IntegrateCellValue<double(TinyVector<1>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_1d,
+                                                             zone_cell_list);
+
+      CellValue<double> cell_value{mesh_1d->connectivity()};
+      cell_value.fill(0);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_1d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<DataType> array =
+        IntegrateCellValue<DataType(TinyVector<1>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_1d,
+                                                               zone_cell_list);
+
+      CellValue<DataType> cell_value{mesh_1d->connectivity()};
+      cell_value.fill(zero);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_1d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<DataType> array =
+        IntegrateCellValue<DataType(TinyVector<1>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_1d,
+                                                               zone_cell_list);
+
+      CellValue<DataType> cell_value{mesh_1d->connectivity()};
+      cell_value.fill(zero);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_1d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<DataType> array =
+        IntegrateCellValue<DataType(TinyVector<1>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_1d,
+                                                               zone_cell_list);
+
+      CellValue<DataType> cell_value{mesh_1d->connectivity()};
+      cell_value.fill(zero);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_1d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<DataType> array =
+        IntegrateCellValue<DataType(TinyVector<1>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_1d,
+                                                               zone_cell_list);
+
+      CellValue<DataType> cell_value{mesh_1d->connectivity()};
+      cell_value.fill(zero);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_1d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<DataType> array =
+        IntegrateCellValue<DataType(TinyVector<1>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_1d,
+                                                               zone_cell_list);
+
+      CellValue<DataType> cell_value{mesh_1d->connectivity()};
+      cell_value.fill(zero);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_1d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<DataType> array =
+        IntegrateCellValue<DataType(TinyVector<1>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_1d,
+                                                               zone_cell_list);
+
+      CellValue<DataType> cell_value{mesh_1d->connectivity()};
+      cell_value.fill(zero);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_1d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, DataType>&>(*discrete_function)));
+    }
+  }
+
+  SECTION("2D")
+  {
+    constexpr size_t Dimension = 2;
+
+    std::shared_ptr<const IQuadratureDescriptor> quadrature_descriptor = std::make_shared<GaussQuadratureDescriptor>(3);
+
+    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]);
+    auto zone_cell_list = mesh_cell_zone.cellList();
+
+    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);
+
+      Array<double> array =
+        IntegrateCellValue<double(TinyVector<2>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_2d,
+                                                             zone_cell_list);
+
+      CellValue<double> cell_value{mesh_2d->connectivity()};
+      cell_value.fill(0);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_2d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<double> array =
+        IntegrateCellValue<double(TinyVector<2>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_2d,
+                                                             zone_cell_list);
+
+      CellValue<double> cell_value{mesh_2d->connectivity()};
+      cell_value.fill(0);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_2d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<double> array =
+        IntegrateCellValue<double(TinyVector<2>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_2d,
+                                                             zone_cell_list);
+
+      CellValue<double> cell_value{mesh_2d->connectivity()};
+      cell_value.fill(0);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_2d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<double> array =
+        IntegrateCellValue<double(TinyVector<2>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_2d,
+                                                             zone_cell_list);
+
+      CellValue<double> cell_value{mesh_2d->connectivity()};
+      cell_value.fill(0);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_2d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<DataType> array =
+        IntegrateCellValue<DataType(TinyVector<2>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_2d,
+                                                               zone_cell_list);
+
+      CellValue<DataType> cell_value{mesh_2d->connectivity()};
+      cell_value.fill(zero);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_2d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<DataType> array =
+        IntegrateCellValue<DataType(TinyVector<2>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_2d,
+                                                               zone_cell_list);
+
+      CellValue<DataType> cell_value{mesh_2d->connectivity()};
+      cell_value.fill(zero);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_2d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<DataType> array =
+        IntegrateCellValue<DataType(TinyVector<2>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_2d,
+                                                               zone_cell_list);
+
+      CellValue<DataType> cell_value{mesh_2d->connectivity()};
+      cell_value.fill(zero);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_2d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<DataType> array =
+        IntegrateCellValue<DataType(TinyVector<2>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_2d,
+                                                               zone_cell_list);
+
+      CellValue<DataType> cell_value{mesh_2d->connectivity()};
+      cell_value.fill(zero);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_2d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<DataType> array =
+        IntegrateCellValue<DataType(TinyVector<2>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_2d,
+                                                               zone_cell_list);
+
+      CellValue<DataType> cell_value{mesh_2d->connectivity()};
+      cell_value.fill(zero);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_2d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<DataType> array =
+        IntegrateCellValue<DataType(TinyVector<2>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_2d,
+                                                               zone_cell_list);
+
+      CellValue<DataType> cell_value{mesh_2d->connectivity()};
+      cell_value.fill(zero);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_2d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, DataType>&>(*discrete_function)));
+    }
+  }
+
+  SECTION("3D")
+  {
+    constexpr size_t Dimension = 3;
+
+    std::shared_ptr<const IQuadratureDescriptor> quadrature_descriptor = std::make_shared<GaussQuadratureDescriptor>(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]);
+    auto zone_cell_list = mesh_cell_zone.cellList();
+
+    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);
+
+      Array<double> array =
+        IntegrateCellValue<double(TinyVector<3>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_3d,
+                                                             zone_cell_list);
+
+      CellValue<double> cell_value{mesh_3d->connectivity()};
+      cell_value.fill(0);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_3d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<double> array =
+        IntegrateCellValue<double(TinyVector<3>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_3d,
+                                                             zone_cell_list);
+
+      CellValue<double> cell_value{mesh_3d->connectivity()};
+      cell_value.fill(0);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_3d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<double> array =
+        IntegrateCellValue<double(TinyVector<3>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_3d,
+                                                             zone_cell_list);
+
+      CellValue<double> cell_value{mesh_3d->connectivity()};
+      cell_value.fill(0);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_3d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<double> array =
+        IntegrateCellValue<double(TinyVector<3>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_3d,
+                                                             zone_cell_list);
+
+      CellValue<double> cell_value{mesh_3d->connectivity()};
+      cell_value.fill(0);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_3d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<DataType> array =
+        IntegrateCellValue<DataType(TinyVector<3>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_3d,
+                                                               zone_cell_list);
+
+      CellValue<DataType> cell_value{mesh_3d->connectivity()};
+      cell_value.fill(zero);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_3d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<DataType> array =
+        IntegrateCellValue<DataType(TinyVector<3>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_3d,
+                                                               zone_cell_list);
+
+      CellValue<DataType> cell_value{mesh_3d->connectivity()};
+      cell_value.fill(zero);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_3d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<DataType> array =
+        IntegrateCellValue<DataType(TinyVector<3>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_3d,
+                                                               zone_cell_list);
+
+      CellValue<DataType> cell_value{mesh_3d->connectivity()};
+      cell_value.fill(zero);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_3d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<DataType> array =
+        IntegrateCellValue<DataType(TinyVector<3>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_3d,
+                                                               zone_cell_list);
+
+      CellValue<DataType> cell_value{mesh_3d->connectivity()};
+      cell_value.fill(zero);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_3d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<DataType> array =
+        IntegrateCellValue<DataType(TinyVector<3>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_3d,
+                                                               zone_cell_list);
+
+      CellValue<DataType> cell_value{mesh_3d->connectivity()};
+      cell_value.fill(zero);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_3d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      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);
+
+      Array<DataType> array =
+        IntegrateCellValue<DataType(TinyVector<3>)>::integrate(function_symbol_id, *quadrature_descriptor, *mesh_3d,
+                                                               zone_cell_list);
+
+      CellValue<DataType> cell_value{mesh_3d->connectivity()};
+      cell_value.fill(zero);
+
+      parallel_for(
+        zone_cell_list.size(), PUGS_LAMBDA(const size_t i) {
+          const CellId cell_id = zone_cell_list[i];
+          cell_value[cell_id]  = array[i];
+        });
+
+      DiscreteFunctionIntegrator integrator(mesh_3d, zone_list, quadrature_descriptor, function_symbol_id);
+      std::shared_ptr discrete_function = integrator.integrate();
+
+      REQUIRE(
+        same_cell_value(cell_value, dynamic_cast<const DiscreteFunctionP0<Dimension, DataType>&>(*discrete_function)));
+    }
+  }
+}