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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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: 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 $ {L_2}$ norm on the boundaries, and some superconvergence results for the single layer potential.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1990-0995213-6
PII: S 0025-5718(1990)0995213-6
Keywords: Collocation method, first-kind boundary integral equations, polygonal regions
Article copyright: © Copyright 1990 American Mathematical Society