THE G METHOD FOR HETEROGENEOUS ANISOTROPIC DIFFUSION ON GENERAL MESHES

被引：38
作者：
Agelas, Leo [1 ]
Di Pietro, Daniele A. [1 ]
Droniou, Jerome [2 ]
机构：
[1] IFP, F-92852 Rueil Malmaison, France
[2] Univ Montpellier 2, Inst Math & Modelisat Montpellier, F-34095 Montpellier 05, France
来源：
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2010年 / 44卷 / 04期
关键词：
Finite volume methods; heterogeneous anisotropic diffusion; MPFA; convergence analysis; FINITE-VOLUME SCHEME; CONVERGENCE;
D O I：
10.1051/m2an/2010021
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：597 / 625
页数：29
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