A Family of Mimetic Finite Difference Methods on Polygonal and Polyhedral Meshes

Franco Brezzi brezzi@cut.this.part.imati.cnr.it

Konstantin Lipnikov lipnikov@cut.this.part.lanl.gov

Valeria Simoncini valeria@cut.this.part.dm.unibo.it

We gave a rigorous mathematical description of a family of mimetic finite difference (MFD) discretizations for diffusion problems on unstructured polygonal and polyhedral meshes. We developed a computationally cheap method for generating particular members of this family. With this new method, the discretizations on polygonal and polyhedral meshes look as simple as discretizations on simplicial meshes. The resulting MFD methods have optimal convergence rates for full material tensors.