An a posteriori error indicator for discontinuous Galerkin approximations of fourth-order elliptic problems

被引：55

作者：

Georgoulis, Emmanuil H. ^{[1
]}

Houston, Paul ^{[2
]}

Virtanen, Juha ^{[1
]}

机构：

[1] Univ Leicester, Dept Math, Leicester LE1 7RH, Leics, England

[2] Univ Nottingham, Sch Math Sci, Nottingham NG7 2RD, England

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2011年 / 31卷 / 01期

关键词：

Discontinuous Galerkin methods; biharmonic problem; fourth order PDEs; a posteriori error analysis; adaptivity; FINITE-ELEMENT APPROXIMATIONS; FAMILY; PLATES;

D O I：

10.1093/imanum/drp023

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a residual-based a posteriori error indicator for discontinuous Galerkin discretizations of the biharmonic equation with essential boundary conditions. We show that the indicator is both reliable and efficient with respect to the approximation error measured in terms of a natural energy norm under minimal regularity assumptions. We validate the performance of the indicator within an adaptive mesh refinement procedure and show its asymptotic exactness for a range of test problems.

引用

页码：281 / 298

页数：18

共 31 条

[1] A posteriori error estimates for fourth-order elliptic problems
Adjerid, S
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2002, 191 (23-24) : 2539 - 2559
[2] A posteriori error estimation for discontinuous Galerkin finite element approximation
Ainsworth, Mark
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2007, 45 (04) : 1777 - 1798
[3] [Anonymous], 2001, E W J NUMER MATH
[4] [Anonymous], 2008, FRONTIERS APPL MATH
[5] Unified analysis of discontinuous Galerkin methods for elliptic problems
Arnold, DN
Brezzi, F
Cockburn, B
Marini, LD
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 39 (05) : 1749 - 1779
[6] BAKER GA, 1977, MATH COMPUT, V31, P45, DOI 10.1090/S0025-5718-1977-0431742-5
[7] Energy norm a posteriori error estimation for discontinuous Galerkin methods
Becker, R
Hansbo, P
Larson, MG
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2003, 192 (5-6) : 723 - 733
[8] C0 interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
Brenner, SC
Sung, LY
[J]. JOURNAL OF SCIENTIFIC COMPUTING, 2005, 22-3 (01) : 83 - 118
[9] BRENNER SC, 2009, IMA J NUMER IN PRESS
[10] Brezzi F., 1991, MIXED HYBRID FINITE, V15

← 1 2 3 4 →