Weighted error estimates of the continuous interior penalty method for singularly perturbed problems

被引：22

作者：

Burman, Erik ^{[2
]}

Guzman, Johnny ^{[1
]}

Leykekhman, Dmitriy ^{[3
]}

机构：

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

[2] Univ Sussex, Dept Math, Brighton BN1 9RF, E Sussex, England

[3] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2009年 / 29卷 / 02期

关键词：

singularly perturbed; convection-diffusion; local error analysis; continuous interior penalty method; FINITE-ELEMENT METHODS; ADVECTION;

D O I：

10.1093/imanum/drn001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we analyse local properties of the continuous interior penalty (CIP) method for a model convection-dominated singularly perturbed convection-diffusion problem. We show weighted a priori error estimates, where the weight function exponentially decays outside the subdomain of interest. This result shows thats locally, the CIP method is comparable to the streamline-diffusion or the discontinuous Galerkin methods.

引用

页码：284 / 314

页数：31

共 17 条

[1]

Becker R, 2004, NUMERICAL MATHEMATICS AND ADVANCED APPLICATIONS, PROCEEDINGS, P123

[2] A unified analysis for conforming and nonconforming stabilized finite element methods using interior penalty [J].

Burman, E .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2005, 43 (05) :2012-2033

[3] Edge stabilization for Galerkin approximations of convection-diffusion-reaction problems [J].

Burman, E ;

Hansbo, P .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2004, 193 (15-16) :1437-1453

[4] Continuous interior penalty hp-finite element methods for advection and advection-diffusion equations [J].

Burman, Erik ;

Ern, Alexandre .

MATHEMATICS OF COMPUTATION, 2007, 76 (259) :1119-1140

[5] Continuous interior penalty finite element method for Oseen's equations [J].

Burman, Erik ;

Fernandez, Miguel A. ;

Hansbo, Peter .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2006, 44 (03) :1248-1274

[6]

Ciarlet Philippe G., 2002, Finite Element Method for Elliptic Problems

[7]

CLEMENT P, 1975, REV FR AUTOMAT INFOR, V9, P77

[8]

Codina R., 2002, Computing and Visualization in Science, V4, P167, DOI 10.1007/s007910100068

[9]

Douglas T., 1976, Methods in Applied Sciences, Lecture Notes inPhysics, V58, P207

[10]

Grisvard P., 1992, Singularities in Boundary Value Problems. Research Notes in Applied Mathematics

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