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Galerkin's method for boundary integral equations on polygonal domains

Published online by Cambridge University Press:  17 February 2009

G. A. Chandler
G. A. Chandler
Affiliation:
Department of Mathematics, University of Queensland, St. Lucia, Queensland 4067.
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Abstract

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A harmonic function in the interior of a polygon is the double layer potential of a distribution satisfying a second kind integral equation. This may be solved numerically by Galerkin's method using piecewise polynomials as basis functions. But the corners produce singularities in the distribution and the kernel of the integral equation; and these reduce the order of convergence. This is offset by grading the mesh, and the orders of convergence and superconvergence are restored to those for a smooth boundary.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 26 , Issue 1 , July 1984, pp. 1 - 13
Copyright
Copyright © Australian Mathematical Society 1984

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