The G method for heterogeneous anisotropic diffusion on general meshes

Agélas, Léo; Di Pietro, Daniele A.; Droniou, Jérôme

ESAIM: Modélisation mathématique et analyse numérique, Tome 44 (2010) no. 4, pp. 597-625.

In the present work we introduce a new family of cell-centered Finite Volume schemes for anisotropic and heterogeneous diffusion operators inspired by the MPFA L method. A very general framework for the convergence study of finite volume methods is provided and then used to establish the convergence of the new method. Fairly general meshes are covered and a computable sufficient criterion for coercivity is provided. In order to guarantee consistency in the presence of heterogeneous diffusivity, we introduce a non-standard test space in $H_0^1$(Ω) and prove its density. Thorough assessment on a set of anisotropic heterogeneous problems as well as a comparison with classical multi-point Finite Volume methods is provided.

Classification : 65N08, 65N12
Mots clés : finite volume methods, heterogeneous anisotropic diffusion, MPFA, convergence analysis

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