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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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The collocation method for first-kind boundary integral equations on polygonal regions
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by Yi Yan PDF
Math. Comp. 54 (1990), 139-154 Request permission

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
  • © Copyright 1990 American Mathematical Society
  • Journal: Math. Comp. 54 (1990), 139-154
  • MSC: Primary 65N35; Secondary 65R20
  • DOI: https://doi.org/10.1090/S0025-5718-1990-0995213-6
  • MathSciNet review: 995213