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Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2010

The G method for heterogeneous anisotropic diffusion on general meshes

Léo Agélas
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Daniele Antonio Di Pietro

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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Dates and versions

hal-00342739 , version 1 (28-11-2008)

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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, 2010, 44 (4), pp.597-625. ⟨10.1051/m2an/2010021⟩. ⟨hal-00342739⟩
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