Convergence of Finite Volume MPFA O type Schemes for Heterogeneous Anisotropic Diffusion Problems on General Meshes

In this paper we prove the convergence of the finite volume MultiPoint Flux Approximation (MPFA) O scheme for anisotropic and heterogeneous diffusion problems. Our framework is based on a discrete hybrid varia- tional formulation which generalizes the usual construction of the MPFA O scheme. The well-posedness and convergence of the scheme is derived assuming a local coercivity condition which can be easily checked numerically. The novel feature of our framework is that it holds for general polygonal and polyhedral meshes as well as for L∞ diffusion coefficients, which is essential in many practical applications.

Key words : Finite Volume, MPFA, Convergence Analysis, Diffusion Equation, Full Tensor, Anisotropy, Heterogeneities, General Meshes

Paper presented by T. Gallouet on December, 29, 2010