A UNIFIED FRAMEWORK FOR TIME-DEPENDENT SINGULARLY PERTURBED PROBLEMS WITH DISCONTINUOUS GALERKIN METHODS IN TIME

被引：6

作者：

Franz, Sebastian ^{[1
]}

Matthies, Gunar ^{[2
]}

机构：

[1] Tech Univ Dresden, Inst Comp Sci, D-01062 Dresden, Germany

[2] Tech Univ Dresden, Inst Numer Math, D-01062 Dresden, Germany

来源：

MATHEMATICS OF COMPUTATION | 2018年 / 87卷 / 313期

关键词：

CONVECTION-DIFFUSION PROBLEMS; INTERIOR PENALTY METHOD; FINITE-ELEMENT-METHOD; HIGHER-ORDER DISCRETISATIONS; SHISHKIN MESHES; CHARACTERISTIC LAYERS; SUPERCONVERGENCE; STABILIZATION; SUPERCLOSENESS; APPROXIMATIONS;

D O I：

10.1090/mcom/3326

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we present a unified framework for the error analysis of time-dependent singularly perturbed problems with discontinuous Galerkin time discretisation. Its general analysis relies on spatial error estimates known from stationary problems and the properties of the discontinuous Galerkin time discretisation. We present also applications of our framework to second- and fourth-order singularly perturbed problems in estimation and simulation.

引用

页码：2113 / 2132

页数：20

共 35 条

[1] Anisotropic mesh refinement for a singularly perturbed reaction diffusion model problem [J].

Apel, T ;

Lube, G .

APPLIED NUMERICAL MATHEMATICS, 1998, 26 (04) :415-433

[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] Weighted error estimates of the continuous interior penalty method for singularly perturbed problems [J].

Burman, Erik ;

Guzman, Johnny ;

Leykekhman, Dmitriy .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2009, 29 (02) :284-314

[5] A fractional step method on a special mesh for the resolution of multidimensional evolutionary convection-diffusion problems [J].

Clavero, C ;

Jorge, JC ;

Lisbona, F ;

Shishkin, GI .

APPLIED NUMERICAL MATHEMATICS, 1998, 27 (03) :211-231

[6] Supercloseness on graded meshes for Q1 finite element approximation of a reaction-diffusion equation [J].

Duran, R. G. ;

Lombardi, A. L. ;

Prieto, M. I. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2013, 242 :232-247

[7] Continuous interior penalty method on a Shishkin mesh for convection-diffusion problems with characteristic boundary layers [J].

Franz, S. .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2008, 197 (45-48) :3679-3686

[8] Superconvergence analysis of the Galerkin FEM for a singularly perturbed convection-diffusion problem with characteristic layers [J].

Franz, Sebastian ;

Linss, Torsten .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2008, 24 (01) :144-164

[9] Superconvergence of a Galerkin FEM for Higher-Order Elements in Convection-Diffusion Problems [J].

Franz, Sebastian ;

Roos, H. -G. .

NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2014, 7 (03) :356-373

[10] A C0 Interior Penalty Method for a Singularly-Perturbed Fourth-Order Elliptic Problem on a Layer-Adapted Mesh [J].

Franz, Sebastian ;

Roos, Hans-Goerg ;

Wachtel, Andreas .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2014, 30 (03) :838-861

← 1 2 3 4 →