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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 2020 MCQ for Mathematics of Computation is 1.78.

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On the convergence of the $p$-version of the boundary element Galerkin method
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by E. P. Stephan and M. Suri PDF
Math. Comp. 52 (1989), 31-48 Request permission

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 ${H^{1/2}}$ and ${H^{ - 1/2}}$-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.
References
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 52 (1989), 31-48
  • MSC: Primary 65R20
  • DOI: https://doi.org/10.1090/S0025-5718-1989-0947469-5
  • MathSciNet review: 947469