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On the convergence of the $ p$-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 $ {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.


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DOI: https://doi.org/10.1090/S0025-5718-1989-0947469-5
Article copyright: © Copyright 1989 American Mathematical Society