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

Léo Agélas (1) , Roland Masson (1)

1 IFPEN - IFP Energies nouvelles

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 variational 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 $L^{\infty}$ diffusion coefficients, which is essential in many practical applications.

Domaines: Analyse numérique [math.NA]

Léo Agélas, Roland Masson. Convergence of Finite Volume MPFA O type Schemes for Heterogeneous Anisotropic Diffusion Problems on General Meshes. 2008. ⟨hal-00340159v1⟩