Home page > 12. Volume 7 N°2 (2010) > Convergence of Finite Volume MPFA O type Schemes for Heterogeneous (...)

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

Wednesday 29 December 2010, by Agélas Léo, Guichard Cindy, Masson Roland

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

logo_hal Voir sur HAL : https://hal.archives-ouvertes.fr/hal-00340159

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