The collocation method for first-kind boundary integral equations on polygonal regions

Author:
Yi Yan

Journal:
Math. Comp. **54** (1990), 139-154

MSC:
Primary 65N35; Secondary 65R20

MathSciNet review:
995213

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper the collocation method for first-kind boundary integral equations, by using piecewise constant trial functions with uniform mesh, is shown to be equivalent to a projection method for second-kind Fredholm equations. In a certain sense this projection is an interpolation projection. By introducing this technique of analysis, we particularly consider the case of polygonal boundaries. We give asymptotic error estimates in norm on the boundaries, and some superconvergence results for the single layer potential.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1990-0995213-6

Keywords:
Collocation method,
first-kind boundary integral equations,
polygonal regions

Article copyright:
© Copyright 1990
American Mathematical Society