A new finite volume scheme for anisotropic diffusion problems on general grids:: convergence analysis

被引:46
作者
Eymard, Robert [1 ]
Gallouet, Thierry
Herbin, Raphaele
机构
[1] Univ Marne la Vallee, F-77454 Marne La Vallee 2, France
[2] Univ Aix Marseille 1, F-13453 Marseille 13, France
关键词
OPERATORS;
D O I
10.1016/j.crma.2007.01.024
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We introduce here a new finite volume scheme which was developed for the discretization of anisotropic diffusion problems; the originality of this scheme lies in the fact that we are able to prove its convergence under very weak assumptions on the discretization mesh.
引用
收藏
页码:403 / 406
页数:4
相关论文
共 7 条
[1]  
Coudière Y, 1999, RAIRO-MATH MODEL NUM, V33, P493
[2]   Discrete Sobolev inequalities and Lp error estimates for finite volume solutions of convection diffusion equations [J].
Coudière, Y ;
Gallouët, T ;
Herbin, R .
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2001, 35 (04) :767-778
[3]   A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids [J].
Domelevo, K ;
Omnes, P .
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2005, 39 (06) :1203-1249
[4]   A cell-centred finite-volume approximation for anisotropic diffusion operators on unstructured meshes in any space dimension [J].
Eymard, R ;
Gallouët, T ;
Herbin, R .
IMA JOURNAL OF NUMERICAL ANALYSIS, 2006, 26 (02) :326-353
[5]   H-convergence and numerical schemes for elliptic problems [J].
Eymard, R ;
Gallouët, T .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2003, 41 (02) :539-562
[6]  
Herbin R., 1995, NUMER METH PARTIAL D, V11, P165
[7]   Finite volume scheme for highly anisotropic diffusion operators on unstructured meshes. [J].
Le Potier, C .
COMPTES RENDUS MATHEMATIQUE, 2005, 340 (12) :921-926