Pointwise Error Estimates for the LDG Method Applied to 1-d Singularly Perturbed Reaction-Diffusion Problems

被引：8

作者：

Zhu, Huiqing ^{[1
]}

Zhang, Zhimin ^{[2
,3
]}

机构：

[1] Univ So Mississippi, Dept Math, Hattiesburg, MS 39406 USA

[2] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

[3] Beijing Computat Sci Res Ctr, Beijing 100084, Peoples R China

来源：

COMPUTATIONAL METHODS IN APPLIED MATHEMATICS | 2013年 / 13卷 / 01期

基金：

美国国家科学基金会;

关键词：

Local Discontinuous Galerkin Method; Singular Perturbed; Shishkin Mesh; DISCONTINUOUS GALERKIN METHOD; HP-VERSION; SUPERCONVERGENCE; DISCRETIZATION;

D O I：

10.1515/cmam-2012-0004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The local discontinuous Galerkin method (LDG) is considered for solving one-dimensional singularly perturbed two-point boundary value problems of reaction-diffusion type. Pointwise error estimates for the LDG approximation to the solution and its derivative are established on a Shishkin-type mesh. Numerical experiments are presented. Moreover, a superconvergence of order 2k + 1 of the numerical traces is observed numerically.

引用

页码：79 / 94

页数：16

共 15 条

[1] Unified analysis of discontinuous Galerkin methods for elliptic problems
Arnold, DN
Brezzi, F
Cockburn, B
Marini, LD
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 39 (05) : 1749 - 1779
[2] Castillo P, 2002, MATH COMPUT, V71, P455, DOI 10.1090/S0025-5718-01-01317-5
[3] Celiker F, 2006, MATH COMPUT, V76, P67
[4] Nodal Superconvergence of SDFEM for Singularly Perturbed Problems
Celiker, Fatih
Zhang, Zhimin
Zhu, Huiqing
[J]. JOURNAL OF SCIENTIFIC COMPUTING, 2012, 50 (02) : 405 - 433
[5] Chen L, 2005, CONTEMP MATH, V383, P191
[6] JOHNSON C, 1986, MATH COMPUT, V46, P1, DOI 10.1090/S0025-5718-1986-0815828-4
[7] Larsson S., 2003, Partial Differential Equations with Numerical Methods
[8] DISCONTINUOUS DISCRETIZATION FOR LEAST-SQUARES FORMULATION OF SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEMS IN ONE AND TWO DIMENSIONS
Lin, Runchang
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2008, 47 (01) : 89 - 108
[9] Miller J.J.H., 2012, Fitted Numerical Methods for Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions
[10] Roos HG, 2008, SPR SER COMPUT MATH, V24, P1

← 1 2 →