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 Ω with boundary Γ may be reformulated as a second kind integral equation on Γ. 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/n2) convergence is obtained for the solution of the integral equation and the associated solution to the Dirichlet problem at any x∈Ω. We present a simple extrapolation scheme which increases these rates of convergence to O(1/n4) .
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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