diff --git a/ProcessLib/AbstractJacobianAssembler.h b/ProcessLib/AbstractJacobianAssembler.h
index db456d9fb84a13f2c3fbb6fa626536d120e658c0..11a91b18b7f34070f32f075a60c5e08a0eeeba3f 100644
--- a/ProcessLib/AbstractJacobianAssembler.h
+++ b/ProcessLib/AbstractJacobianAssembler.h
@@ -32,7 +32,7 @@ public:
 
     //! Assembles the Jacobian, the matrices \f$M\f$ and \f$K\f$, and the vector
     //! \f$b\f$ with coupling.
-    virtual void assembleWithJacobianAndCoupling(
+    virtual void assembleWithJacobianForStaggeredScheme(
         LocalAssemblerInterface& /*local_assembler*/, double const /*t*/,
         std::vector<double> const& /*local_xdot*/, const double /*dxdot_dx*/,
         const double /*dx_dx*/, std::vector<double>& /*local_M_data*/,
diff --git a/ProcessLib/AnalyticalJacobianAssembler.cpp b/ProcessLib/AnalyticalJacobianAssembler.cpp
index 87160943710b742215ab39c85f0e609301531b63..fd686e3d187412b7b3aee8611aa4e2eeba58d792 100644
--- a/ProcessLib/AnalyticalJacobianAssembler.cpp
+++ b/ProcessLib/AnalyticalJacobianAssembler.cpp
@@ -25,7 +25,7 @@ void AnalyticalJacobianAssembler::assembleWithJacobian(
                                          local_b_data, local_Jac_data);
 }
 
-void AnalyticalJacobianAssembler::assembleWithJacobianAndCoupling(
+void AnalyticalJacobianAssembler::assembleWithJacobianForStaggeredScheme(
     LocalAssemblerInterface& local_assembler, double const t,
     std::vector<double> const& local_xdot, const double dxdot_dx,
     const double dx_dx, std::vector<double>& local_M_data,
@@ -33,7 +33,7 @@ void AnalyticalJacobianAssembler::assembleWithJacobianAndCoupling(
     std::vector<double>& local_Jac_data,
     LocalCoupledSolutions const& local_coupled_solutions)
 {
-    local_assembler.assembleWithJacobianAndCoupling(
+    local_assembler.assembleWithJacobianForStaggeredScheme(
         t, local_xdot, dxdot_dx, dx_dx, local_M_data, local_K_data,
         local_b_data, local_Jac_data, local_coupled_solutions);
 }
diff --git a/ProcessLib/AnalyticalJacobianAssembler.h b/ProcessLib/AnalyticalJacobianAssembler.h
index 45c6d01f7e1c5a2bbe7ed0edaf5f53b6fac12ca6..005f3b0ae2287ca30e0f59cdabaf6d0423807755 100644
--- a/ProcessLib/AnalyticalJacobianAssembler.h
+++ b/ProcessLib/AnalyticalJacobianAssembler.h
@@ -38,7 +38,7 @@ public:
         std::vector<double>& local_K_data, std::vector<double>& local_b_data,
         std::vector<double>& local_Jac_data) override;
 
-    void assembleWithJacobianAndCoupling(
+    void assembleWithJacobianForStaggeredScheme(
         LocalAssemblerInterface& local_assembler,
         double const t, std::vector<double> const& local_xdot,
         const double dxdot_dx, const double dx_dx,
diff --git a/ProcessLib/HT/StaggeredHTFEM-impl.h b/ProcessLib/HT/StaggeredHTFEM-impl.h
index 9bd6806f4b475f06c401e25c0fb94af2e3a9adb9..bdd0c2074bb4844587f2587c1b28ac32115e5fdf 100644
--- a/ProcessLib/HT/StaggeredHTFEM-impl.h
+++ b/ProcessLib/HT/StaggeredHTFEM-impl.h
@@ -24,7 +24,7 @@ namespace HT
 template <typename ShapeFunction, typename IntegrationMethod,
           unsigned GlobalDim>
 void StaggeredHTFEM<ShapeFunction, IntegrationMethod, GlobalDim>::
-    assembleWithCoupledTerm(double const t,
+    assembleForStaggeredScheme(double const t,
                             std::vector<double>& local_M_data,
                             std::vector<double>& local_K_data,
                             std::vector<double>& local_b_data,
diff --git a/ProcessLib/HT/StaggeredHTFEM.h b/ProcessLib/HT/StaggeredHTFEM.h
index 947452a97c447fe452483e80972d5d51033acdc4..d9296be17add4161be26819fc6ae357818240d33 100644
--- a/ProcessLib/HT/StaggeredHTFEM.h
+++ b/ProcessLib/HT/StaggeredHTFEM.h
@@ -62,7 +62,7 @@ public:
     {
     }
 
-    void assembleWithCoupledTerm(
+    void assembleForStaggeredScheme(
         double const t, std::vector<double>& local_M_data,
         std::vector<double>& local_K_data, std::vector<double>& local_b_data,
         LocalCoupledSolutions const& coupled_xs) override;
diff --git a/ProcessLib/HydroMechanics/HydroMechanicsFEM-impl.h b/ProcessLib/HydroMechanics/HydroMechanicsFEM-impl.h
index e47bb62d4e5e976c32774b5225e070a1018c909a..086d620796027ed78ffbc38895b05e40139c6b72 100644
--- a/ProcessLib/HydroMechanics/HydroMechanicsFEM-impl.h
+++ b/ProcessLib/HydroMechanics/HydroMechanicsFEM-impl.h
@@ -215,7 +215,7 @@ template <typename ShapeFunctionDisplacement, typename ShapeFunctionPressure,
 void HydroMechanicsLocalAssembler<ShapeFunctionDisplacement,
                                   ShapeFunctionPressure, IntegrationMethod,
                                   DisplacementDim>::
-    assembleWithJacobianAndCoupling(
+    assembleWithJacobianForStaggeredScheme(
         const double t,
         const std::vector<double>& local_xdot,
         const double dxdot_dx,
diff --git a/ProcessLib/HydroMechanics/HydroMechanicsFEM.h b/ProcessLib/HydroMechanics/HydroMechanicsFEM.h
index 253e4062d24b8b6a61a4d215c52fc21a60d98efc..435f9ffe5b676d88542f031a7e7e88278a186379 100644
--- a/ProcessLib/HydroMechanics/HydroMechanicsFEM.h
+++ b/ProcessLib/HydroMechanics/HydroMechanicsFEM.h
@@ -356,7 +356,7 @@ public:
             .noalias() += Kup * p;
     }
 
-    void assembleWithJacobianAndCoupling(
+    void assembleWithJacobianForStaggeredScheme(
         double const t, std::vector<double> const& local_xdot,
         const double dxdot_dx, const double dx_dx,
         std::vector<double>& local_M_data, std::vector<double>& local_K_data,
diff --git a/ProcessLib/LocalAssemblerInterface.cpp b/ProcessLib/LocalAssemblerInterface.cpp
index 937cfbd387a74b5516b0ba7608a3d197619ba3a8..b23bf60c6b31b48f4b2c2280e68fa215f9829ce0 100644
--- a/ProcessLib/LocalAssemblerInterface.cpp
+++ b/ProcessLib/LocalAssemblerInterface.cpp
@@ -25,7 +25,7 @@ void LocalAssemblerInterface::assemble(double const /*t*/,
         "The assemble() function is not implemented in the local assembler.");
 }
 
-void LocalAssemblerInterface::assembleWithCoupledTerm(
+void LocalAssemblerInterface::assembleForStaggeredScheme(
     double const /*t*/,
     std::vector<double>& /*local_M_data*/,
     std::vector<double>& /*local_K_data*/,
@@ -33,7 +33,7 @@ void LocalAssemblerInterface::assembleWithCoupledTerm(
     LocalCoupledSolutions const& /*coupled_solutions*/)
 {
     OGS_FATAL(
-        "The assembleWithCoupledTerm() function is not implemented in the "
+        "The assembleForStaggeredScheme() function is not implemented in the "
         "local assembler.");
 }
 
@@ -50,7 +50,7 @@ void LocalAssemblerInterface::assembleWithJacobian(
         "assembler.");
 }
 
-void LocalAssemblerInterface::assembleWithJacobianAndCoupling(
+void LocalAssemblerInterface::assembleWithJacobianForStaggeredScheme(
     double const /*t*/, std::vector<double> const& /*local_xdot*/,
     const double /*dxdot_dx*/, const double /*dx_dx*/,
     std::vector<double>& /*local_M_data*/,
@@ -60,7 +60,7 @@ void LocalAssemblerInterface::assembleWithJacobianAndCoupling(
     LocalCoupledSolutions const& /*local_coupled_solutions*/)
 {
     OGS_FATAL(
-        "The assembleWithJacobianAndCoupling() function is not implemented in"
+        "The assembleWithJacobianForStaggeredScheme() function is not implemented in"
         " the local assembler.");
 }
 
diff --git a/ProcessLib/LocalAssemblerInterface.h b/ProcessLib/LocalAssemblerInterface.h
index 94e0d82dd3ae96c17556c2f35c9f6c82f5890e91..eda17c0f65a52233e44875213c2af783db54393d 100644
--- a/ProcessLib/LocalAssemblerInterface.h
+++ b/ProcessLib/LocalAssemblerInterface.h
@@ -40,7 +40,7 @@ public:
                           std::vector<double>& local_K_data,
                           std::vector<double>& local_b_data);
 
-    virtual void assembleWithCoupledTerm(
+    virtual void assembleForStaggeredScheme(
         double const t,
         std::vector<double>& local_M_data,
         std::vector<double>& local_K_data,
@@ -56,7 +56,7 @@ public:
                                       std::vector<double>& local_b_data,
                                       std::vector<double>& local_Jac_data);
 
-    virtual void assembleWithJacobianAndCoupling(
+    virtual void assembleWithJacobianForStaggeredScheme(
         double const t, std::vector<double> const& local_xdot,
         const double dxdot_dx, const double dx_dx,
         std::vector<double>& local_M_data, std::vector<double>& local_K_data,
diff --git a/ProcessLib/VectorMatrixAssembler.cpp b/ProcessLib/VectorMatrixAssembler.cpp
index e167bdee25918b8f1faa53d8c85eb082698873f6..a88fb8bcf40d0bca7a29cc9a220e56b0cc9b37b7 100644
--- a/ProcessLib/VectorMatrixAssembler.cpp
+++ b/ProcessLib/VectorMatrixAssembler.cpp
@@ -75,9 +75,9 @@ void VectorMatrixAssembler::assemble(
             cpl_xs->dt, cpl_xs->process_id, std::move(local_coupled_xs0),
             std::move(local_coupled_xs));
 
-        local_assembler.assembleWithCoupledTerm(t, _local_M_data, _local_K_data,
-                                                _local_b_data,
-                                                local_coupled_solutions);
+        local_assembler.assembleForStaggeredScheme(t, _local_M_data,
+                                                   _local_K_data, _local_b_data,
+                                                   local_coupled_solutions);
     }
 
     auto const num_r_c = indices.size();
@@ -138,9 +138,9 @@ void VectorMatrixAssembler::assembleWithJacobian(
     {
         if (base_dof_table == nullptr)
         {
-            localAssembleWithJacobianAndCoupling(t, indices, indices,
-                                                 local_xdot, local_assembler,
-                                                 dxdot_dx, dx_dx, cpl_xs);
+            local_assembleWithJacobianForStaggeredScheme(
+                t, indices, indices, local_xdot, local_assembler, dxdot_dx,
+                dx_dx, cpl_xs);
         }
         else
         {
@@ -149,7 +149,7 @@ void VectorMatrixAssembler::assembleWithJacobian(
             {
                 const auto base_indices =
                     NumLib::getIndices(mesh_item_id, *base_dof_table);
-                localAssembleWithJacobianAndCoupling(
+                local_assembleWithJacobianForStaggeredScheme(
                     t, base_indices, indices, local_xdot, local_assembler,
                     dxdot_dx, dx_dx, cpl_xs);
             }
@@ -157,7 +157,7 @@ void VectorMatrixAssembler::assembleWithJacobian(
             {
                 const auto full_indices =
                     NumLib::getIndices(mesh_item_id, dof_table);
-                localAssembleWithJacobianAndCoupling(
+                local_assembleWithJacobianForStaggeredScheme(
                     t, indices, full_indices, local_xdot, local_assembler,
                     dxdot_dx, dx_dx, cpl_xs);
             }
@@ -197,7 +197,7 @@ void VectorMatrixAssembler::assembleWithJacobian(
     }
 }
 
-void VectorMatrixAssembler::localAssembleWithJacobianAndCoupling(
+void VectorMatrixAssembler::local_assembleWithJacobianForStaggeredScheme(
     const double t, std::vector<GlobalIndexType> const& base_indices,
     std::vector<GlobalIndexType> const& full_indices,
     std::vector<double> const& local_xdot,
@@ -222,7 +222,7 @@ void VectorMatrixAssembler::localAssembleWithJacobianAndCoupling(
         cpl_xs->dt, cpl_xs->process_id, std::move(local_coupled_xs0),
         std::move(local_coupled_xs));
 
-    _jacobian_assembler->assembleWithJacobianAndCoupling(
+    _jacobian_assembler->assembleWithJacobianForStaggeredScheme(
         local_assembler, t, local_xdot, dxdot_dx, dx_dx, _local_M_data,
         _local_K_data, _local_b_data, _local_Jac_data, local_coupled_solutions);
 }
diff --git a/ProcessLib/VectorMatrixAssembler.h b/ProcessLib/VectorMatrixAssembler.h
index 0f41b856681b80622bef07f2c098e4e5d811931b..01af18a628609a282e997f37aa5ae1864304f5a0 100644
--- a/ProcessLib/VectorMatrixAssembler.h
+++ b/ProcessLib/VectorMatrixAssembler.h
@@ -71,7 +71,7 @@ private:
     //! Used to assemble the Jacobian.
     std::unique_ptr<AbstractJacobianAssembler> _jacobian_assembler;
 
-    void localAssembleWithJacobianAndCoupling(
+    void local_assembleWithJacobianForStaggeredScheme(
         const double t, std::vector<GlobalIndexType> const& base_indices,
         std::vector<GlobalIndexType> const& full_indices,
         std::vector<double> const& local_xdot,