Technical Note: A note on the selection of the penalty parameter for discontinuous Galerkin finite element schemes

被引：17

作者：

Ainsworth, Mark ^{[1
]}

Rankin, Richard ^{[1
]}

机构：

[1] Univ Strathclyde, Dept Math & Stat, Glasgow G1 1XH, Lanark, Scotland

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2012年 / 28卷 / 03期

关键词：

discontinuous Galerkin method; finite element; interior penalty method; ADVECTION-DIFFUSION EQUATIONS; HANGING NODES; ERROR-BOUNDS; APPROXIMATION; MESHES;

D O I：

10.1002/num.20663

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain a computable lower bound on the value of the interior penalty parameters sufficient for the existence of a unique discontinuous Galerkin finite element approximation of a second order elliptic problem. The bound obtained is valid for meshes containing an arbitrary number of hanging nodes and elements of arbitrary nonuniform polynomial order. (c) 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011

引用

页码：1099 / 1104

页数：6

共 10 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] Constant free error bounds for nonuniform order discontinuous Galerkin finite-element approximation on locally refined meshes with hanging nodes [J].

Ainsworth, Mark ;

Rankin, Richard .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2011, 31 (01) :254-280

[3] FULLY COMPUTABLE ERROR BOUNDS FOR DISCONTINUOUS GALERKIN FINITE ELEMENT APPROXIMATIONS ON MESHES WITH AN ARBITRARY NUMBER OF LEVELS OF HANGING NODES [J].

Ainsworth, Mark ;

Rankin, Richard .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2010, 47 (06) :4112-4141

[4] 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

[5] Estimation of penalty parameters for symmetric interior penalty Galerkin methods [J].

Epshteyn, Yekaterina ;

Riviere, Beatrice .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 206 (02) :843-872

[6]

Ern A, 2008, J COMPUT MATH, V26, P488

[7] A discontinuous Galerkin method with weighted averages for advection-diffusion equations with locally small and anisotropic diffusivity [J].

Ern, Alexandre ;

Stephansen, Annette F. ;

Zunino, Paolo .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2009, 29 (02) :235-256

[8]

Hughes TJR, 2000, LECT NOTES COMP SCI, V11, P135

[9] An explicit expression for the penalty parameter of the interior penalty method [J].

Shahbazi, K .

JOURNAL OF COMPUTATIONAL PHYSICS, 2005, 205 (02) :401-407

[10] On the constants in hp-finite element trace inverse inequalities [J].

Warburton, T ;

Hesthaven, JS .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2003, 192 (25) :2765-2773

← 1 →