Convergence analysis of the mimetic finite difference method for elliptic problems

We propose a family of mimetic discretization schemes for elliptic problems including convection and reaction terms. Our approach is an extension of the mimetic methodology for purely diffusive problems on unstructured polygonal and polyhedral meshes. The a priori error analysis relies on the connection between the mimetic formulation and the lowest order Raviart–Thomas mixed finite element method. The theoretical results are confirmed by numerical experiments.