Year: 1992
Author: I.G. Graham, Qun Lin, Rui-Feng Xie
Journal of Computational Mathematics, Vol. 10 (1992), Iss. 3 : pp. 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 $O(1/n^4)$ .
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1992-JCM-9356
Journal of Computational Mathematics, Vol. 10 (1992), Iss. 3 : pp. 231–244
Published online: 1992-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14