Uniform Superconvergence of Galerkin Methods for Singularly Perturbed Problems

Uniform Superconvergence of Galerkin Methods for Singularly Perturbed Problems

Year:    2010

Journal of Computational Mathematics, Vol. 28 (2010), Iss. 2 : pp. 273–288

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2009.10-m2870

Journal of Computational Mathematics, Vol. 28 (2010), Iss. 2 : pp. 273–288

Published online:    2010-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

Keywords:    singularly perturbed Hermite splines Shishkin-type meshes Interpolation post-processing Uniform superconvergence.