On the convergence of the -version of the boundary element Galerkin method

Authors:
E. P. Stephan and M. Suri

Journal:
Math. Comp. **52** (1989), 31-48

MSC:
Primary 65R20

DOI:
https://doi.org/10.1090/S0025-5718-1989-0947469-5

MathSciNet review:
947469

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Abstract: We prove convergence for the *p*-version of Galerkin boundary element schemes applied to various first-kind integral equations. We establish optimal error estimates for the *p*-version in the and -norms and also derive rates of convergence in slightly stronger norms when the exact nature of the singularity of the solution is known. Our results lead to a boundary element method for two-dimensional screen problems in acoustics, which has twice the rate of convergence of the usual *h*-version with uniform mesh. An application to three-dimensional exterior problems is also analyzed.

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DOI:
https://doi.org/10.1090/S0025-5718-1989-0947469-5

Article copyright:
© Copyright 1989
American Mathematical Society