diff --git a/dumux/discretization/box/fvgridgeometry.hh b/dumux/discretization/box/fvgridgeometry.hh
index 2da6f459167432d0349cbab4690d3803e9d83d31..02c490081eaa10e6bce105c87e75ebaf51ec493a 100644
--- a/dumux/discretization/box/fvgridgeometry.hh
+++ b/dumux/discretization/box/fvgridgeometry.hh
@@ -180,9 +180,14 @@ public:
     { return periodicVertexMap_.at(dofIdx); }
 
     //! Returns the map between dofs across periodic boundaries
-    const std::unordered_map<GridIndexType, GridIndexType>& periodicVertexMap() const
+    const std::unordered_map<GridIndexType, GridIndexType>& periodicDofMap() const
     { return periodicVertexMap_; }
 
+    //! Returns the map between dofs across periodic boundaries
+    [[deprecated("Will be removed after release 3.9. Use periodicDofMap() instead.")]]
+    const std::unordered_map<GridIndexType, GridIndexType>& periodicVertexMap() const
+    { return periodicDofMap(); }
+
     //! local view of this object (constructed with the internal cache)
     friend inline LocalView localView(const BoxFVGridGeometry& gg)
     { return { gg.cache_ }; }
@@ -529,9 +534,14 @@ public:
     { return periodicVertexMap_.at(dofIdx); }
 
     //! Returns the map between dofs across periodic boundaries
-    const std::unordered_map<GridIndexType, GridIndexType>& periodicVertexMap() const
+    const std::unordered_map<GridIndexType, GridIndexType>& periodicDofMap() const
     { return periodicVertexMap_; }
 
+    //! Returns the map between dofs across periodic boundaries
+    [[deprecated("Will be removed after release 3.9. Use periodicDofMap() instead.")]]
+    const std::unordered_map<GridIndexType, GridIndexType>& periodicVertexMap() const
+    { return periodicDofMap(); }
+
     //! local view of this object (constructed with the internal cache)
     friend inline LocalView localView(const BoxFVGridGeometry& gg)
     { return { gg.cache_ }; }
diff --git a/dumux/discretization/facecentered/diamond/fvgridgeometry.hh b/dumux/discretization/facecentered/diamond/fvgridgeometry.hh
index 0c7b2bab6c3ca92ff43f1bfd8d180ecee6b49409..5adb2e41d48877cdb8b5f7bc3d996b6f37c4f729 100644
--- a/dumux/discretization/facecentered/diamond/fvgridgeometry.hh
+++ b/dumux/discretization/facecentered/diamond/fvgridgeometry.hh
@@ -165,10 +165,15 @@ public:
     GridIndexType periodicallyMappedDof(GridIndexType dofIdx) const
     { return periodicFaceMap_.at(dofIdx); }
 
-    //! Returns the map between dofs across periodic boundaries // TODO rename to periodic dof map in fvassembler
-    const std::unordered_map<GridIndexType, GridIndexType>& periodicVertexMap() const
+    //! Returns the map between dofs across periodic boundaries
+    const std::unordered_map<GridIndexType, GridIndexType>& periodicDofMap() const
     { return periodicFaceMap_; }
 
+    //! Returns the map between dofs across periodic boundaries
+    [[deprecated("Will be removed after release 3.9. Use periodicDofMap() instead.")]]
+    const std::unordered_map<GridIndexType, GridIndexType>& periodicVertexMap() const
+    { return periodicDofMap(); }
+
     //! local view of this object (constructed with the internal cache)
     friend inline LocalView localView(const FaceCenteredDiamondFVGridGeometry& gg)
     { return { gg.cache_ }; }
diff --git a/dumux/discretization/facecentered/staggered/fvgridgeometry.hh b/dumux/discretization/facecentered/staggered/fvgridgeometry.hh
index abf11397eb4d3673ff594c5fa9a14af552f73e9d..41d58c51ff969be0aec89f2c01bb53f6d5894fb0 100644
--- a/dumux/discretization/facecentered/staggered/fvgridgeometry.hh
+++ b/dumux/discretization/facecentered/staggered/fvgridgeometry.hh
@@ -241,10 +241,15 @@ public:
     GridIndexType periodicallyMappedDof(GridIndexType dofIdx) const
     { return periodicFaceMap_.at(dofIdx); }
 
-    //! Returns the map between dofs across periodic boundaries // TODO rename to periodic dof map in fvassembler
-    const std::unordered_map<GridIndexType, GridIndexType>& periodicVertexMap() const
+    //! Returns the map between dofs across periodic boundaries
+    const std::unordered_map<GridIndexType, GridIndexType>& periodicDofMap() const
     { return periodicFaceMap_; }
 
+    //! Returns the map between dofs across periodic boundaries
+    [[deprecated("Will be removed after release 3.9. Use periodicDofMap() instead.")]]
+    const std::unordered_map<GridIndexType, GridIndexType>& periodicVertexMap() const
+    { return periodicDofMap(); }
+
 private:
 
     void update_()
@@ -644,10 +649,15 @@ public:
     GridIndexType periodicallyMappedDof(GridIndexType dofIdx) const
     { return periodicFaceMap_.at(dofIdx); }
 
-    //! Returns the map between dofs across periodic boundaries // TODO rename to periodic dof map in fvassembler
-    const std::unordered_map<GridIndexType, GridIndexType>& periodicVertexMap() const
+    //! Returns the map between dofs across periodic boundaries
+    const std::unordered_map<GridIndexType, GridIndexType>& periodicDofMap() const
     { return periodicFaceMap_; }
 
+    //! Returns the map between dofs across periodic boundaries
+    [[deprecated("Will be removed after release 3.9. Use periodicDofMap() instead.")]]
+    const std::unordered_map<GridIndexType, GridIndexType>& periodicVertexMap() const
+    { return periodicDofMap(); }
+
 private:
 
     void update_()
diff --git a/dumux/discretization/fem/fegridgeometry.hh b/dumux/discretization/fem/fegridgeometry.hh
index 100c3ba8225112d4aec28d47318eb40548db5ded..e50d06854569ad1621196ba1e371ae505b73b8fe 100644
--- a/dumux/discretization/fem/fegridgeometry.hh
+++ b/dumux/discretization/fem/fegridgeometry.hh
@@ -98,6 +98,7 @@ public:
     { DUNE_THROW(Dune::NotImplemented, "Periodic BC support for FEM schemes"); }
 
     //! Returns the map between dofs across periodic boundaries
+    [[deprecated("Will be removed after release 3.9. Implement periodicDofMap() if periodic bcs are supported.")]]
     const std::unordered_map<GridIndexType, GridIndexType>& periodicVertexMap() const
     { DUNE_THROW(Dune::NotImplemented, "Periodic BC support for FEM schemes"); }
 
diff --git a/dumux/discretization/porenetwork/gridgeometry.hh b/dumux/discretization/porenetwork/gridgeometry.hh
index 5687e8accbf182b1b753e1e5e7f7ea0b88f64924..788ad2203421c2e80ff4ca4ac3721eae55877437 100644
--- a/dumux/discretization/porenetwork/gridgeometry.hh
+++ b/dumux/discretization/porenetwork/gridgeometry.hh
@@ -589,6 +589,7 @@ public:
     { DUNE_THROW(Dune::NotImplemented, "Periodic boundaries"); }
 
     //! Returns the map between dofs across periodic boundaries
+    [[deprecated("Will be removed after release 3.9. Implement periodicDofMap() if periodic bcs are supported.")]]
     std::unordered_map<GridIndexType, GridIndexType> periodicVertexMap() const
     { return std::unordered_map<GridIndexType, GridIndexType>{}; }
 
@@ -783,6 +784,7 @@ public:
     { DUNE_THROW(Dune::NotImplemented, "Periodic boundaries"); }
 
     //! Returns the map between dofs across periodic boundaries
+    [[deprecated("Will be removed after release 3.9. Implement periodicDofMap() if periodic bcs are supported.")]]
     std::unordered_map<GridIndexType, GridIndexType> periodicVertexMap() const
     { return std::unordered_map<GridIndexType, GridIndexType>{}; }
 
diff --git a/dumux/discretization/pq1bubble/fvgridgeometry.hh b/dumux/discretization/pq1bubble/fvgridgeometry.hh
index 2d18705167470dcd21469a29f731b4aebee4061f..c8bd0df6275fedefaccaaff3a3da07dd27788d58 100644
--- a/dumux/discretization/pq1bubble/fvgridgeometry.hh
+++ b/dumux/discretization/pq1bubble/fvgridgeometry.hh
@@ -185,9 +185,14 @@ public:
     { return periodicVertexMap_.at(dofIdx); }
 
     //! Returns the map between dofs across periodic boundaries
-    const std::unordered_map<GridIndexType, GridIndexType>& periodicVertexMap() const
+    const std::unordered_map<GridIndexType, GridIndexType>& periodicDofMap() const
     { return periodicVertexMap_; }
 
+    //! Returns the map between dofs across periodic boundaries
+    [[deprecated("Will be removed after release 3.9. Use periodicDofMap() instead.")]]
+    const std::unordered_map<GridIndexType, GridIndexType>& periodicVertexMap() const
+    { return periodicDofMap(); }
+
     //! local view of this object (constructed with the internal cache)
     friend inline LocalView localView(const PQ1BubbleFVGridGeometry& gg)
     { return { gg.cache_ }; }
diff --git a/dumux/multidomain/facet/box/fvgridgeometry.hh b/dumux/multidomain/facet/box/fvgridgeometry.hh
index c598c85a7dd35901b4c83e0f9cfad38d2318b1f9..c76793740f741f4ec3b7cc1f07c93e4b5b5945bf 100644
--- a/dumux/multidomain/facet/box/fvgridgeometry.hh
+++ b/dumux/multidomain/facet/box/fvgridgeometry.hh
@@ -219,6 +219,7 @@ public:
     { DUNE_THROW(Dune::InvalidStateException, "Periodic boundaries are not supported by the box facet coupling scheme"); }
 
     //! Returns the map between dofs across periodic boundaries
+    [[deprecated("Will be removed after release 3.9. Implement periodicDofMap() if periodic bcs are supported.")]]
     std::unordered_map<GridIndexType, GridIndexType> periodicVertexMap() const
     { return std::unordered_map<GridIndexType, GridIndexType>(); }
 
@@ -509,6 +510,7 @@ public:
     { DUNE_THROW(Dune::InvalidStateException, "Periodic boundaries are not supported by the facet coupling scheme"); }
 
     //! Returns the map between dofs across periodic boundaries
+    [[deprecated("Will be removed after release 3.9. Implement periodicDofMap() if periodic bcs are supported.")]]
     std::unordered_map<GridIndexType, GridIndexType> periodicVertexMap() const
     { return std::unordered_map<GridIndexType, GridIndexType>(); }
 
diff --git a/dumux/porousmediumflow/boxdfm/fvgridgeometry.hh b/dumux/porousmediumflow/boxdfm/fvgridgeometry.hh
index dc4717eac7fd711da27f0be3b5757a3894814c72..ed4fb89bae07503a08f392d354ddeb4e8f13ec1a 100644
--- a/dumux/porousmediumflow/boxdfm/fvgridgeometry.hh
+++ b/dumux/porousmediumflow/boxdfm/fvgridgeometry.hh
@@ -192,6 +192,7 @@ public:
     { DUNE_THROW(Dune::InvalidStateException, "Periodic boundaries are not supported by the box-dfm scheme"); }
 
     //! Returns the map between dofs across periodic boundaries
+    [[deprecated("Will be removed after release 3.9. Implement periodicDofMap() if periodic bcs are supported.")]]
     std::unordered_map<std::size_t, std::size_t> periodicVertexMap() const
     { return std::unordered_map<std::size_t, std::size_t>(); }
 
@@ -516,6 +517,7 @@ public:
     { DUNE_THROW(Dune::InvalidStateException, "Periodic boundaries are not supported by the box-dfm scheme"); }
 
     //! Returns the map between dofs across periodic boundaries
+    [[deprecated("Will be removed after release 3.9. Implement periodicDofMap() if periodic bcs are supported.")]]
     std::unordered_map<std::size_t, std::size_t> periodicVertexMap() const
     { return std::unordered_map<std::size_t, std::size_t>(); }