A brief survey on numerical methods for solving singularly perturbed problems

被引：160

作者：

Kadalbajoo, Mohan K. ^{[1
]}

Gupta, Vikas ^{[2
]}

机构：

[1] Indian Inst Technol, Dept Math & Stat, Kanpur 208016, Uttar Pradesh, India

[2] BITS Pilani, Grp Math, Goa 403726, India

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2010年 / 217卷 / 08期

关键词：

Singular perturbation; Boundary layers; Layer adapted meshes; Uniform convergence; BOUNDARY-VALUE-PROBLEMS; FINITE-ELEMENT-METHOD; CONVECTION-DIFFUSION PROBLEM; ORDINARY DIFFERENTIAL-EQUATIONS; SPLINE COLLOCATION METHOD; UNIFORM POINTWISE CONVERGENCE; DISCONTINUOUS GALERKIN METHOD; POSTERIORI ERROR ESTIMATION; ANISOTROPIC MESH REFINEMENT; LAYER-ADAPTED MESHES;

D O I：

10.1016/j.amc.2010.09.059

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper, a brief survey on computational techniques for the different classes of singularly perturbed problems is given. This survey is a continuation of work performed earlier by the first author and contains the literature of the work done by the researchers during the years 2000-2009. However some older important relevant papers are also included in this survey. We also mentioned those papers which are not surveyed in the previous survey papers by the first author of this paper, see [Appl. Math. Comput. 30 (1989) 223-259, 130 (2002) 457-510, 134 (2003) 371-429] for details. Thus this survey paper contains a surprisingly large amount of literature on singularly perturbed problems and indeed can serve as an introduction to some of the ideas and methods for the singular perturbation problems. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：3641 / 3716

页数：76

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