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

被引：51

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 50 条

[21] Convergence of adaptive discontinuous Galerkin approximations of second-order elliptic problems
Karakashian, Ohannes A.
Pascal, Frederic
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2007, 45 (02) : 641 - 665
[22] A POSTERIORI ERROR ESTIMATES FOR A LOCAL DISCONTINUOUS GALERKIN APPROXIMATION OF SEMILINEAR SECOND-ORDER ELLIPTIC PROBLEMS ON CARTESIAN GRIDS
Baccouch, Mahboub
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2023, 20 (06) : 772 - 804
[23] A priori and a posteriori error analysis for discontinuous Galerkin finite element approximations of biharmonic eigenvalue problems
Liang Wang
Chunguang Xiong
Huibin Wu
Fusheng Luo
Advances in Computational Mathematics, 2019, 45 : 2623 - 2646
[24] A posteriori error estimation and dynamic adaptivity for symmetric discontinuous Galerkin approximations of reactive transport problems
Sun, SY
Wheeler, MF
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2006, 195 (7-8) : 632 - 652
[25] A DISCONTINUOUS GALERKIN METHOD FOR THE FOURTH-ORDER CURL PROBLEM
Hong, Qingguo
Hu, Jun
Shu, Shi
Xu, Jinchao
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2012, 30 (06) : 565 - 578
[26] A priori and a posteriori error analysis for discontinuous Galerkin finite element approximations of biharmonic eigenvalue problems
Wang, Liang
Xiong, Chunguang
Wu, Huibin
Luo, Fusheng
ADVANCES IN COMPUTATIONAL MATHEMATICS, 2019, 45 (5-6) : 2623 - 2646
[27] A priori and a posteriori error analysis for the mixed discontinuous Galerkin finite element approximations of the biharmonic problems
Xiong, Chunguang
Becker, Roland
Luo, Fusheng
Ma, Xiuling
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2017, 33 (01) : 318 - 353
[28] A discontinuous Galerkin method and its error estimate for nonlinear fourth-order wave equations
Tao, Qi
Xu, Yan
Shu, Chi-Wang
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2021, 386
[29] A posteriori error estimation for adaptive discontinuous Galerkin approximations of hyperbolic systems
Larson, MG
Barth, TJ
DISCONTINUOUS GALERKIN METHODS: THEORY, COMPUTATION AND APPLICATIONS, 2000, 11 : 363 - 368
[30] A POSTERIORI ERROR ANALYSIS OF EULER-GALERKIN APPROXIMATIONS TO COUPLED ELLIPTIC-PARABOLIC PROBLEMS
Ern, Alexandre
Meunier, Sebastien
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2009, 43 (02): : 353 - 375

← 1 2 3 4 5 →