On the convergence of collocation methods for Symm's integral equation on open curves

Authors:
M. Costabel, V. J. Ervin and E. P. Stephan

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

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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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DOI:
https://doi.org/10.1090/S0025-5718-1988-0942148-1

Article copyright:
© Copyright 1988
American Mathematical Society