diff --git a/src/mesh/Connectivity.cpp b/src/mesh/Connectivity.cpp
index fedd337467e4418f70a1ec87a9547f433bff0672..b588f30c56e0afea05821ad025ba794508fc1197 100644
--- a/src/mesh/Connectivity.cpp
+++ b/src/mesh/Connectivity.cpp
@@ -158,7 +158,7 @@ void Connectivity<3>::_computeFaceCellConnectivities()
   m_connectivity_computer.computeInverseConnectivityMatrix(cell_to_face_matrix,
                                                            face_to_cell_matrix);
 
-  m_face_to_cell_local_face
+  m_face_local_numbers_in_their_cells
       = m_connectivity_computer.computeLocalItemNumberInChildItem<ItemType::face,
                                                                   ItemType::cell>(*this);
 
@@ -278,10 +278,10 @@ Connectivity(const std::vector<std::vector<unsigned int>>& cell_by_node_vector)
   m_connectivity_computer.computeInverseConnectivityMatrix(cell_to_node_matrix,
                                                            node_to_cell_matrix);
 
-  m_node_to_cell_local_node
+  m_node_local_numbers_in_their_cells
       = m_connectivity_computer.computeLocalItemNumberInChildItem<ItemType::node, ItemType::cell>(*this);
 
-  m_cell_to_node_local_cell
+  m_cell_local_numbers_in_their_nodes
       = m_connectivity_computer.computeLocalItemNumberInChildItem<ItemType::cell, ItemType::node>(*this);
 
   if constexpr (Dimension>1) {
diff --git a/src/mesh/Connectivity.hpp b/src/mesh/Connectivity.hpp
index 0bb4501ca3d9b45065dd6000273629c1b077ef11..b40c1ec181e8447de4c152d2af3ce154c0b159c1 100644
--- a/src/mesh/Connectivity.hpp
+++ b/src/mesh/Connectivity.hpp
@@ -248,30 +248,29 @@ class Connectivity final
     return m_cell_face_is_reversed;
   }
 
-  [[deprecated("These member functions are poorly named")]]
-  const auto& cellToNodeLocalCell() const
+  const auto& cellLocalNumbersInTheirNodes() const
   {
-    return m_cell_to_node_local_cell;
+    return m_cell_local_numbers_in_their_nodes;
   }
 
-  const auto& nodeToCellLocalNode() const
+  const auto& nodeLocalNumbersInTheirCells() const
   {
-    return m_node_to_cell_local_node;
+    return m_node_local_numbers_in_their_cells;
   }
 
-  const auto& faceToCellLocalFace() const
+  const auto& faceLocalNumbersInTheirCells() const
   {
     if constexpr(dimension>1) {
-      return m_face_to_cell_local_face;
+      return m_face_local_numbers_in_their_cells;
     } else {
-      return m_node_to_cell_local_node;
+      return m_node_local_numbers_in_their_cells;
     }
   }
 
   const auto& nodeToFaceLocalNode() const
   {
-    static_assert("this function has no meaning in 1d");
-    return m_node_to_face_local_node;
+    static_assert(Dimension==1,"this function has no meaning in 1d");
+    return m_node_local_numbers_in_their_faces;
   }
 
 private:
@@ -279,17 +278,16 @@ private:
 
   FaceValuePerCell<const bool> m_cell_face_is_reversed;
 
-  [[deprecated("These members are poorly named")]]
-  NodeValuePerCell<const unsigned short> m_cell_to_node_local_cell;
+  NodeValuePerCell<const unsigned short> m_cell_local_numbers_in_their_nodes;
 
-  CellValuePerFace<const unsigned short> m_face_to_cell_local_face;
+  CellValuePerFace<const unsigned short> m_face_local_numbers_in_their_cells;
 
-  CellValuePerNode<const unsigned short> m_node_to_cell_local_node;
+  CellValuePerNode<const unsigned short> m_node_local_numbers_in_their_cells;
 
   // not plugged ...
 #warning remaining def
-  NodeValuePerFace<unsigned short> m_node_to_face_local_node;
-  FaceValuePerNode<unsigned short> m_face_to_node_local_face;
+  NodeValuePerFace<unsigned short> m_node_local_numbers_in_their_faces;
+  FaceValuePerNode<unsigned short> m_face_local_numbers_in_their_nodes;
   // ... not plugged
 
   ConnectivityComputer m_connectivity_computer;
diff --git a/src/scheme/AcousticSolver.hpp b/src/scheme/AcousticSolver.hpp
index 52a3905c1746d90f71a1946c9a0b4fb982213eab..4145c01ea62352436fecbe43ce33983e0db19143 100644
--- a/src/scheme/AcousticSolver.hpp
+++ b/src/scheme/AcousticSolver.hpp
@@ -101,14 +101,18 @@ class AcousticSolver
     const auto& node_to_cell_matrix
         = getConnectivityMatrix<ItemType::node,
                                 ItemType::cell>(m_connectivity);
-    const auto& node_to_cell_local_node = m_connectivity.nodeToCellLocalNode();
+    const auto& node_local_numbers_in_their_cells
+        = m_connectivity.nodeLocalNumbersInTheirCells();
+
     Kokkos::parallel_for(m_mesh.numberOfNodes(), KOKKOS_LAMBDA(const int& r) {
         Rdd sum = zero;
         const auto& node_to_cell = node_to_cell_matrix.rowConst(r);
-        const auto& cell_local_node = node_to_cell_local_node.itemValues(r);
+        const auto& node_local_number_in_its_cells
+            = node_local_numbers_in_their_cells.itemValues(r);
+
         for (size_t j=0; j<node_to_cell.length; ++j) {
           const unsigned int J = node_to_cell(j);
-          const unsigned int R = cell_local_node[j];
+          const unsigned int R = node_local_number_in_its_cells[j];
           sum += Ajr(J,R);
         }
         m_Ar(r) = sum;
@@ -126,15 +130,18 @@ class AcousticSolver
     const auto& node_to_cell_matrix
         = getConnectivityMatrix<ItemType::node,
                                 ItemType::cell>(m_connectivity);
-    const auto& node_to_cell_local_node = m_connectivity.nodeToCellLocalNode();
+    const auto& node_local_numbers_in_their_cells
+        = m_connectivity.nodeLocalNumbersInTheirCells();
+
     Kokkos::parallel_for(m_mesh.numberOfNodes(), KOKKOS_LAMBDA(const int& r) {
         Rd& br = m_br(r);
         br = zero;
         const auto& node_to_cell = node_to_cell_matrix.rowConst(r);
-        const auto& cell_local_node = node_to_cell_local_node.itemValues(r);
+        const auto& node_local_number_in_its_cells
+            = node_local_numbers_in_their_cells.itemValues(r);
         for (size_t j=0; j<node_to_cell.length; ++j) {
           const unsigned int J = node_to_cell(j);
-          const unsigned int R = cell_local_node[j];
+          const unsigned int R = node_local_number_in_its_cells[j];
           br += Ajr(J,R)*uj(J) + pj(J)*Cjr(J,R);
         }
       });