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The G method for heterogeneous anisotropic diffusionon general meshes

Published online by Cambridge University Press:  17 March 2010

Léo Agélas ,
Daniele A. Di Pietro  and
Jérôme Droniou
Léo Agélas
Affiliation:
IFP, 1 & 4 av. du Bois-Préau, 92852 Rueil-Malmaison Cedex, France. leo.agelas@ifp.fr; daniele-antonio.di-pietro@ifp.fr
Daniele A. Di Pietro
Affiliation:
IFP, 1 & 4 av. du Bois-Préau, 92852 Rueil-Malmaison Cedex, France. leo.agelas@ifp.fr; daniele-antonio.di-pietro@ifp.fr
Jérôme Droniou
Affiliation:
Université Montpellier 2, Institut de Mathématiques et Modélisation de Montpellier, CC 051, Place Eugène Bataillon, 34095 Montpellier Cedex 05, France. droniou@math.univ-montp2.fr
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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 $H_0^1$ (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.

Keywords

Finite volume methodsheterogeneous anisotropic diffusionMPFAconvergence analysis

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Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 44 , Issue 4 , July 2010 , pp. 597 - 625
Copyright
© EDP Sciences, SMAI, 2010

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