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Volume 10, Issue 3
Extrapolation of Nyström Solutions of Boundary Integral Equations on Non-Smooth Domains

I.G. Graham, Qun Lin & Rui-Feng Xie

J. Comp. Math., 10 (1992), pp. 231-244.

Published online: 1992-10

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  • Abstract

The interior Dirichlet problem for Laplace's equation on a plane polygonal region $\Omega$ with boundary $\Gamma$ may be reformulated as a second kind integral equation on $\Gamma$. This equation may be solved by the Nyström method using the composite trapezoidal rule. It is known that if the mesh has $O(n)$ points and is graded appropriately, then $O(1/n^2)$ convergence is obtained for the solution of the integral equation and the associated solution to the Dirichlet problem at any $x\in \Omega$. We present a simple extrapolation scheme which increases these rates of convergence to $O(1/n^4)$ .  

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@Article{JCM-10-231, author = {Graham , I.G.Lin , Qun and Xie , Rui-Feng}, title = {Extrapolation of Nyström Solutions of Boundary Integral Equations on Non-Smooth Domains}, journal = {Journal of Computational Mathematics}, year = {1992}, volume = {10}, number = {3}, pages = {231--244}, abstract = {

The interior Dirichlet problem for Laplace's equation on a plane polygonal region $\Omega$ with boundary $\Gamma$ may be reformulated as a second kind integral equation on $\Gamma$. This equation may be solved by the Nyström method using the composite trapezoidal rule. It is known that if the mesh has $O(n)$ points and is graded appropriately, then $O(1/n^2)$ convergence is obtained for the solution of the integral equation and the associated solution to the Dirichlet problem at any $x\in \Omega$. We present a simple extrapolation scheme which increases these rates of convergence to $O(1/n^4)$ .  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9356.html} }
TY - JOUR T1 - Extrapolation of Nyström Solutions of Boundary Integral Equations on Non-Smooth Domains AU - Graham , I.G. AU - Lin , Qun AU - Xie , Rui-Feng JO - Journal of Computational Mathematics VL - 3 SP - 231 EP - 244 PY - 1992 DA - 1992/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9356.html KW - AB -

The interior Dirichlet problem for Laplace's equation on a plane polygonal region $\Omega$ with boundary $\Gamma$ may be reformulated as a second kind integral equation on $\Gamma$. This equation may be solved by the Nyström method using the composite trapezoidal rule. It is known that if the mesh has $O(n)$ points and is graded appropriately, then $O(1/n^2)$ convergence is obtained for the solution of the integral equation and the associated solution to the Dirichlet problem at any $x\in \Omega$. We present a simple extrapolation scheme which increases these rates of convergence to $O(1/n^4)$ .  

Graham , I.G.Lin , Qun and Xie , Rui-Feng. (1992). Extrapolation of Nyström Solutions of Boundary Integral Equations on Non-Smooth Domains. Journal of Computational Mathematics. 10 (3). 231-244. doi:
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