A Priori and a Posteriori Error Estimates for H(div)-Elliptic Problem with Interior Penalty Method

被引：1

作者：

Zeng, Yuping ^{[1
]}

Chen, Jinru ^{[1
]}

机构：

[1] Nanjing Normal Univ, Sch Math Sci, Jiangsu Key Lab NSLSCS, Nanjing 210023, Jiangsu, Peoples R China

来源：

COMMUNICATIONS IN COMPUTATIONAL PHYSICS | 2013年 / 14卷 / 03期

关键词：

Discontinuous Galerkin method; H(div)-elliptic problem; a priori error estimate; a posteriori error estimate; DISCONTINUOUS GALERKIN METHODS; MIXED FINITE-ELEMENTS; APPROXIMATION; DISCRETIZATIONS; H(DIV);

D O I：

10.4208/cicp.040412.071112a

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we propose and analyze the interior penalty discontinuous Galerkin method for H(div)-elliptic problem. An optimal a priori error estimate in the energy norm is proved. In addition, a residual-based a posteriori error estimator is obtained. The estimator is proved to be both reliable and efficient in the energy norm. Some numerical testes are presented to demonstrate the effectiveness of our method.

引用

页码：753 / 779

页数：27

共 35 条

[1]

Ainsworth M., 2000, PUR AP M-WI

[2] A posteriori error estimation for discontinuous Galerkin finite element approximation [J].

Ainsworth, Mark .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2007, 45 (04) :1777-1798

[3]

[Anonymous], TECHNICAL REPORT

[4]

[Anonymous], 2000, LECT NOTES COMPUTATI

[5]

[Anonymous], 2008, MATH THEORY FINITE E, V105, pA341

[6] Unified analysis of discontinuous Galerkin methods for elliptic problems [J].

Arnold, DN ;

Brezzi, F ;

Cockburn, B ;

Marini, LD .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 39 (05) :1749-1779

[7] Preconditioning in H(div) and applications [J].

Arnold, DN ;

Falk, RS ;

Winther, R .

MATHEMATICS OF COMPUTATION, 1997, 66 (219) :957-984

[8]

Babuska I., 2001, NUMER MATH SCI COMP

[9] Residual based a posteriori error estimators for eddy current computation [J].

Beck, R ;

Hiptmair, R ;

Hoppe, RHW ;

Wohlmuth, B .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2000, 34 (01) :159-182

[10] Energy norm a posteriori error estimation for discontinuous Galerkin methods [J].

Becker, R ;

Hansbo, P ;

Larson, MG .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2003, 192 (5-6) :723-733

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