Pointwise convergence of approximations to a convection-diffusion equation on a Shishkin mesh

被引：14

作者：

Lenferink, W ^{[1
]}

机构：

[1] Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden

来源：

APPLIED NUMERICAL MATHEMATICS | 2000年 / 32卷 / 01期

关键词：

singular perturbation; piecewise equidistant mesh; uniform accuracy;

D O I：

10.1016/S0168-9274(99)00009-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A centered difference or finite element discretization is applied to a singularly perturbed, one-dimensional boundary value problem. The discretization uses a piecewise equidistant mesh. It is proved that the pointwise error is (almost) of second order with respect to the number of nodes, uniformly in the perturbation parameter. The proof is based on a monotonicity argument. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.

引用

页码：69 / 86

页数：18

共 12 条

[1]

ANDREEV WB, 1996, ZH VYCHISL MAT MAT F, V36, P101

[2]

Axelsson O., 1994, ITERATIVE SOLUTION M

[3] ACCURATE DISCRETIZATION FOR SINGULAR PERTURBATIONS - THE ONE-DIMENSIONAL CASE [J].

HU, XC ;

MANTEUFFEL, TA ;

MCCORMICK, S ;

RUSSELL, TF .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1995, 32 (01) :83-109

[4]

LAYTON WJ, MBI964 O VONG U

[5]

MEIS T, 1978, NUMERISCHE BEHANDLUN

[6]

Miller JJ, 2012, Fitted numerical methods for singular perturbation problems

[7]

Roos HG, 1996, NUMERICAL METHODS SI

[8]

SHISHKIN GI, 1992, APPROXIMATION SINGUL

[9] A uniformly convergent galerkin method on a Shishkin mesh for a convection-diffusion problem [J].

Stynes, M ;

ORiordan, E .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 214 (01) :36-54

[10] The midpoint upwind scheme [J].

Stynes, M ;

Roos, HG .

APPLIED NUMERICAL MATHEMATICS, 1997, 23 (03) :361-374

← 1 2 →