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Volume 28, Issue 2
Uniform Superconvergence of Galerkin Methods for Singularly Perturbed Problems

Ying Chen & Min Huang

DOI: 10.4208/jcm.2009.10-m2870

J. Comp. Math., 28 (2010), pp. 273-288.

Published online: 2010-04

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65L10, 65L60.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-28-273, author = {Ying Chen and Min Huang}, title = {Uniform Superconvergence of Galerkin Methods for Singularly Perturbed Problems}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {2}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.10-m2870}, url = {http://global-sci.org/intro/article_detail/jcm/8519.html} }
TY - JOUR T1 - Uniform Superconvergence of Galerkin Methods for Singularly Perturbed Problems AU - Ying Chen & Min Huang JO - Journal of Computational Mathematics VL - 2 SP - 273 EP - 288 PY - 2010 DA - 2010/04 SN - 28 DO - http://doi.org/10.4208/jcm.2009.10-m2870 UR - https://global-sci.org/intro/article_detail/jcm/8519.html KW - singularly perturbed, Hermite splines, Shishkin-type meshes, Interpolation post-processing, Uniform superconvergence. AB -

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.

Ying Chen and Min Huang. (2010). Uniform Superconvergence of Galerkin Methods for Singularly Perturbed Problems. Journal of Computational Mathematics. 28 (2). 273-288. doi:10.4208/jcm.2009.10-m2870
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