The G method for heterogeneous anisotropic diffusion on general meshes

Leo Agelas, Daniele A Di Pietro, Jerome Droniou

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32 Citations (Scopus)

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 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)(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.
Original languageEnglish
Pages (from-to)597 - 625
Number of pages29
JournalEsaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique
Volume44
Issue number4
DOIs
Publication statusPublished - 2010
Externally publishedYes

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