The G method for heterogeneous anisotropic diffusion on general meshes

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...

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Bibliographic Details
Published in:ESAIM. Mathematical modelling and numerical analysis 2010-07, Vol.44 (4), p.597-625
Main Authors: Agélas, Léo, Di Pietro, Daniele A., Droniou, Jérôme
Format: Article
Language:English
Subjects:
65N08
65N12
Anisotropy
Assessments
Coercive force
Convergence
convergence analysis
Diffusion
Exact sciences and technology
Finite element method
Finite volume method
Finite volume methods
heterogeneous anisotropic diffusion
Mathematical analysis
Mathematical models
Mathematics
MPFA
Numerical Analysis
Permeability
Sciences and techniques of general use
Stencils
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Summary: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.
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an/2010021