On the convergence of the 𝑝-version of the boundary element Galerkin method-Reference-Cited by-同舟云学术

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

Published:1989 Issue:185 Volume:52 Page:31-48
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Stephan E. P.,Suri M.

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 {H^{1/2}} and H − 1 / 2 {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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1989-52-185/S0025-5718-1989-0947469-5/S0025-5718-1989-0947469-5.pdf

Reference27 articles.

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4. I, Babuška, The p and h-p Versions of the Finite Element Method. The State of the Art, Technical Note BN-1156, Institute for Physical Science and Technology, University of Maryland, College Park, MD, 1986.

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