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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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On the convergence of collocation methods for Symm’s integral equation on open curves
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by M. Costabel, V. J. Ervin and E. P. Stephan PDF
Math. Comp. 51 (1988), 167-179 Request permission

Abstract:

Recently, Costabel and Stephan in [8] presented convergence proofs for collocation with piecewise linear trial functions for Symm’s integral equation on plane closed curves with corners. In this article we prove the convergence of the above collocation method in the case of open curves. We derive asymptotic error estimates in Sobolev norms and analyze the effect of graded meshes. Numerical experiments based on the implementation of [6] show experimental orders of convergence which confirm our theoretical results on the asymptotic rates of convergence.
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Math. Comp. 51 (1988), 167-179
  • MSC: Primary 65R20; Secondary 45E99, 45L10
  • DOI: https://doi.org/10.1090/S0025-5718-1988-0942148-1
  • MathSciNet review: 942148