The G method for heterogeneous anisotropic diffusion on general meshes

Abstract : 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 coercivity criterion is provided. In order to guarantee consistency in the presence of heterogeneous diffusivity, we introduce a non-standard test space in $H_0^1(\Omega)$ 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.
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ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2010, 44 (4), pp.597-625. 〈10.1051/m2an/2010021〉
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https://hal.archives-ouvertes.fr/hal-00342739
Contributeur : Daniele Antonio Di Pietro <>
Soumis le : vendredi 28 novembre 2008 - 13:02:20
Dernière modification le : jeudi 21 juin 2018 - 14:12:09
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Léo Agélas, Daniele Antonio Di Pietro, Jérôme Droniou. The G method for heterogeneous anisotropic diffusion on general meshes. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2010, 44 (4), pp.597-625. 〈10.1051/m2an/2010021〉. 〈hal-00342739〉

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