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Volume 7, Issue 2
Extrapolation for the Approximations to the Solution of a Boundary Integral Equation on Polygonal Domains

Qun Lin & Rui-Feng Xie

J. Comp. Math., 7 (1989), pp. 174-181.

Published online: 1989-07

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  • Abstract

In this paper, we consider a boundary integral equation of second kind rising from potential theory. The equation may be solved numerically by Galerkin's method using piecewise constant functions. Because of the singularities produced by the corners, we have to grade the mesh near the corner. In general, Chandler obtained the order 2 superconvergence of the iterated Galerkin solution in the uniform norm. It is proved in this paper that the Richardson extrapolation increases the accuracy from order 2 to order 4.  

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@Article{JCM-7-174, author = {Lin , Qun and Xie , Rui-Feng}, title = {Extrapolation for the Approximations to the Solution of a Boundary Integral Equation on Polygonal Domains}, journal = {Journal of Computational Mathematics}, year = {1989}, volume = {7}, number = {2}, pages = {174--181}, abstract = {

In this paper, we consider a boundary integral equation of second kind rising from potential theory. The equation may be solved numerically by Galerkin's method using piecewise constant functions. Because of the singularities produced by the corners, we have to grade the mesh near the corner. In general, Chandler obtained the order 2 superconvergence of the iterated Galerkin solution in the uniform norm. It is proved in this paper that the Richardson extrapolation increases the accuracy from order 2 to order 4.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9467.html} }
TY - JOUR T1 - Extrapolation for the Approximations to the Solution of a Boundary Integral Equation on Polygonal Domains AU - Lin , Qun AU - Xie , Rui-Feng JO - Journal of Computational Mathematics VL - 2 SP - 174 EP - 181 PY - 1989 DA - 1989/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9467.html KW - AB -

In this paper, we consider a boundary integral equation of second kind rising from potential theory. The equation may be solved numerically by Galerkin's method using piecewise constant functions. Because of the singularities produced by the corners, we have to grade the mesh near the corner. In general, Chandler obtained the order 2 superconvergence of the iterated Galerkin solution in the uniform norm. It is proved in this paper that the Richardson extrapolation increases the accuracy from order 2 to order 4.  

Lin , Qun and Xie , Rui-Feng. (1989). Extrapolation for the Approximations to the Solution of a Boundary Integral Equation on Polygonal Domains. Journal of Computational Mathematics. 7 (2). 174-181. doi:
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