UNIFORM SUPERCONVERGENCE OF GALERKIN METHODS FOR SINGULARLY PERTURBED PROBLEMS

In this paper, we are concerned with uniform superconvergence of Galerkin methods for singularly perturbed reaction-diffusion problems by using two Shishkin-type meshes. Based on an estimate of the error between spline interpolation of the exact solution and its numerical approximation, an interpola...

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Bibliographic Details
Published inJournal of computational mathematics Vol. 28; no. 2; pp. 273 - 288
Main Authors Chen, Ying, Huang, Min
Format Journal Article
LanguageEnglish
Published Chinese Academy of Mathematices and System Sciences (AMSS) Chinese Academy of Sciences 01.03.2010
Subjects
Approximation
Boundary value problems
Degrees of polynomials
Embeddings
Estimation methods
Finite element method
Galerkin methods
Galerkin方法
Integers
Interpolation
伽辽金方法
反应扩散问题
后处理技术
奇摄动问题
数值逼近
样条插值
超收敛
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Summary:In this paper, we are concerned with uniform superconvergence of Galerkin methods for singularly perturbed reaction-diffusion problems by using two Shishkin-type meshes. Based on an estimate of the error between spline interpolation of the exact solution and its numerical approximation, an interpolation post-processing technique is applied to the original numerical solution. This results in approximation exhibit superconvergence which is uniform in the weighted energy norm. Numerical examples are presented to demonstrate the effectiveness of the interpolation post-processing technique and to verify the theoretical results obtained in this paper.
Bibliography:singularly perturbed, Hermite splines, Shishkin-type meshes, Interpolation post-processing, Uniform superconvergence.
11-2126/O1
O241.82
O175.29
ISSN:0254-9409
1991-7139
DOI:10.4208/jcm.2009.10-m2870