# Is there any fundamental difference between meshing for FEM, FVM and FDM?

I am a novice to the field of computational science and have just started studying the FDM and FEM (haven't started on FVM yet). While trying the understand the subject I got this question and trying to find an answer over the net did not yield any answer (maybe the question is naive, please bear with me). Is there any fundamental difference between meshing for FEM, FVM (and FDM)?.

I know for FDM the mesh needs to be structured and FEM and FVM can use unstructured mesh too. But can a mesh created for the FEM method be utilized for FVM?. (I have till now always created mesh either for CFD or structural-fea, and the meshing here could be required to have a finer mesh where the gradient is high or to accommodate some turbulence model, etc). But is there any inherent difference between mesh created for FEM and FVM (and FDM)? ie can I use a mesh created for FEM to be solved using FVM? (I have used different types of elements/cells/subdivisions (like different order etc) when solving FEA problems but haven't done anything like that for CFD (using FVM) problem (just different form of elements like tet or hex or prism etc). What are the inherent differences (if any) for meshing for FEM and FVM or is meshing technique same for both?

## 1 Answer

You are correct that FDM requires structured meshes, so you are restricted to those.

On the other hand FEM and FVM can both do structured meshes as well as unstructured meshes depending on the method chosen. And no, in general there is no difference in the meshing required for the two unless you start approaching edge cases such as meshes with polygons in which case possibly finite volumes may be easier to use than finite elements.

To give you an example, Discontinuous Galerkin methods which you may classify as FEM has a strong relationship to FVM. A P0 nodal DG method is essentially a first order FVM while the integrals of higher order nodal DG look very similar to FVM.

• I would be careful, this is not always true. For instance, a meshes used in cell-centered fvm need good orthogonality if you wish to solve a Poisson equation. I don’t think such a criteria applies to Continuous Galerkin FEM for instance.
– BlaB
Jun 6, 2019 at 21:40
• Yes, I agree that its not always true. But usually these are corner cases. Jun 9, 2019 at 13:54