A unifying theory of a posteriori error control for discontinuous Galerkin FEM

被引：35

作者：

Carstensen, Carsten ^{[1
]}

Gudi, Thirupathi ^{[2
]}

Jensen, Max ^{[3
]}

机构：

[1] Humboldt Univ, Dept Math, D-10099 Berlin, Germany

[2] Louisiana State Univ, Ctr Computat & Technol, Baton Rouge, LA 70803 USA

[3] Univ Durham, Sci Labs, Dept Math Sci, Durham DH1 3LE, England

来源：

NUMERISCHE MATHEMATIK | 2009年 / 112卷 / 03期

关键词：

FINITE-ELEMENT-METHOD; APPROXIMATIONS; ELASTICITY;

D O I：

10.1007/s00211-009-0223-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A unified a posteriori error analysis is derived in extension of Carstensen (Numer Math 100: 617-637, 2005) and Carstensen and Hu (J NumerMath 107 (3): 473-502, 2007) for a wide range of discontinuous Galerkin (dG) finite element methods (FEM), applied to the Laplace, Stokes, and Lame equations. Two abstract assumptions (A1) and (A2) guarantee the reliability of explicit residual-based computable error estimators. The edge jumps are recast via lifting operators to make arguments already established for nonconforming finite element methods available. The resulting reliable error estimate is applied to 16 representative dG FEMs from the literature. The estimate recovers known results as well as provides new bounds to a number of schemes.

引用

页码：363 / 379

页数：17

共 34 条

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

Ainsworth, Mark .

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

[2]

[Anonymous], 1997, Finite elements

[3] 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

[4] NONCONFORMING ELEMENTS IN FINITE-ELEMENT METHOD WITH PENALTY [J].

BABUSKA, I ;

ZLAMAL, M .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1973, 10 (05) :863-875

[5] A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations [J].

Bassi, F ;

Rebay, S .

JOURNAL OF COMPUTATIONAL PHYSICS, 1997, 131 (02) :267-279

[6]

Bassi F., 1997, 2 EUROPEAN C TURBOMA, P99

[7] A discontinuous hp finite element method for convection-diffusion problems [J].

Baumann, CE ;

Oden, JT .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1999, 175 (3-4) :311-341

[8] 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

[9] Uniform convergence and a posteriori error estimators for the enhanced strain finite element method [J].

Braess, D ;

Carstensen, C ;

Reddy, BD .

NUMERISCHE MATHEMATIK, 2004, 96 (03) :461-479

[10]

Brezzi F, 2000, NUMER METH PART D E, V16, P365, DOI 10.1002/1098-2426(200007)16:4<365::AID-NUM2>3.0.CO

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