The G method for heterogeneous anisotropic diffusion on general meshes
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 4, p. 597-625

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.

DOI : https://doi.org/10.1051/m2an/2010021
Classification:  65N08,  65N12
Keywords: finite volume methods, heterogeneous anisotropic diffusion, MPFA, convergence analysis
@article{M2AN_2010__44_4_597_0,
     author = {Ag\'elas, L\'eo and Di Pietro, Daniele A. and Droniou, J\'er\^ome},
     title = {The G method for heterogeneous anisotropic diffusion on general meshes},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {4},
     year = {2010},
     pages = {597-625},
     doi = {10.1051/m2an/2010021},
     zbl = {1202.65143},
     mrnumber = {2683575},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2010__44_4_597_0}
}
Agélas, Léo; Di Pietro, Daniele A.; Droniou, Jérôme. The G method for heterogeneous anisotropic diffusion on general meshes. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 4, pp. 597-625. doi : 10.1051/m2an/2010021. http://www.numdam.org/item/M2AN_2010__44_4_597_0/

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