The G method for heterogeneous anisotropic diffusion on general meshes
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2 Université Montpellier 2, Institut de Mathématiques et Modélisation de Montpellier, CC 051, Place Eugène Bataillon, 34095 Montpellier Cedex 05, France. firstname.lastname@example.org
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 (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.
Mathematics Subject Classification: 65N08 / 65N12
Key words: Finite volume methods / heterogeneous anisotropic diffusion / MPFA / convergence analysis
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