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

Abstract : 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.
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Léo Agélas, Cindy Guichard, Roland Masson. Convergence of Finite Volume MPFA O type Schemes for Heterogeneous Anisotropic Diffusion Problems on General Meshes. International Journal on Finite Volumes, Institut de Mathématiques de Marseille, AMU, 2010, pp.volume 7 No 2. ⟨hal-00340159v2⟩

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