A finite element method on composite grids based on Nitsche's method

被引：92

作者：

Hansbo, A

Hansbo, P

Larson, MG

机构：

[1] Univ Trollhattan Uddevalla, Dept Math & Informat, S-46139 Trollhattan, Sweden

[2] Chalmers Univ Technol, Dept Appl Mech, S-41296 Gothenburg, Sweden

[3] Chalmers Univ Technol, Dept Math, S-41296 Gothenburg, Sweden

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2003年 / 37卷 / 03期

关键词：

Nitsche's method; overlapping grids;

D O I：

10.1051/m2an:2003039

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we propose a finite element method for the approximation of second order elliptic problems on composite grids. The method is based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges (or faces) of one the grids. We prove optimal order a priori and energy type a posteriori error estimates in 2 and 3 space dimensions, and present some numerical examples.

引用

页码：495 / 514

页数：20

共 14 条

[1] The mortar element method with overlapping subdomains
Achdou, Y
Maday, Y
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 40 (02) : 601 - 628
[2] [Anonymous], 1979, FINITE ELEMENT APPRO, DOI DOI 10.1007/BFB0063447
[3] A finite element method for domain decomposition with non-matching grids
Becker, R
Hansbo, P
Stenberg, R
[J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2003, 37 (02): : 209 - 225
[4] ON CONSERVATION AT GRID INTERFACES
BERGER, MJ
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1987, 24 (05) : 967 - 984
[5] Brenner S. C., 2007, Texts Appl. Math., V15
[6] Analysis of a Chimera method
Brezzi, F
Lions, JL
Pironneau, O
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2001, 332 (07): : 655 - 660
[7] Overlapping nonmatching grid mortar element methods for elliptic problems
Cai, XC
Dryja, M
Sarkis, M
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1999, 36 (02) : 581 - 606
[8] COMPOSITE OVERLAPPING MESHES FOR THE SOLUTION OF PARTIAL-DIFFERENTIAL EQUATIONS
CHESSHIRE, G
HENSHAW, WD
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 1990, 90 (01) : 1 - 64
[9] An unfitted finite element method, based on Nitsche's method, for elliptic interface problems
Hansbo, A
Hansbo, P
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2002, 191 (47-48) : 5537 - 5552
[10] Lazarov Raytcho D., 2001, COMPUT METH APPL MAT, V1, P367

← 1 2 →