A VIRTUAL VOLUME METHOD FOR HETEROGENEOUS AND ANISOTROPIC DIFFUSION-REACTION PROBLEMS ON GENERAL MESHES

被引：7

作者：

Coatleven, Julien ^{[1
]}

机构：

[1] IFP Energies Nouvelles, 1 & 4 Ave Bois Preau, F-92852 Rueil Malmaison, France

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2017年 / 51卷 / 03期

关键词：

Heterogeneous diffusion-reaction problems; finite volumes; general meshes; virtual element method; UNSTRUCTURED GRIDS; POLYHEDRAL MESHES; DARCY FLOWS; DISCRETIZATION; MEDIA; SCHEME; CONVERGENCE;

D O I：

10.1051/m2an/2016036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Starting from the recently introduced virtual element method, we construct new diffusion fluxes in two and three dimensions that give birth to symmetric, unconditionally coercive finite volume like schemes for the discretization of heterogeneous and anisotropic diffusion-reaction problems on general, possibly nonconforming meshes. Convergence of the approximate solutions is proved for general tensors and meshes. Error estimates are derived under classical regularity assumptions. Numerical results illustrate the performance of the scheme. The link with the original vertex approximate gradient scheme is emphasized.

引用

页码：797 / 824

页数：28

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