Extrapolation of Nyström Solutions of Boundary Integral Equations on Non-Smooth Domains

Extrapolation of Nyström Solutions of Boundary Integral Equations on Non-Smooth Domains

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

Keywords:   

Author Details

I.G. Graham

Qun Lin

Rui-Feng Xie