Efficiency of a posteriori BEM–error estimates for first-kind integral equations on quasi

Efficiency of a posteriori BEM–error estimates for first-kind integral equations on quasi–uniform meshes

Published:1996 Issue:213 Volume:65 Page:69-84
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Carstensen Carsten

Abstract

In the numerical treatment of integral equations of the first kind using boundary element methods (BEM), the author and E. P. Stephan have derived a posteriori error estimates as tools for both reliable computation and self-adaptive mesh refinement. So far, efficiency of those a posteriori error estimates has been indicated by numerical examples in model situations only. This work affirms efficiency by proving the reverse inequality. Based on best approximation, on inverse inequalities and on stability of the discretization, and complementary to our previous work, an abstract approach yields a converse estimate. This estimate proves efficiency of an a posteriori error estimate in the BEM on quasi–uniform meshes for Symm’s integral equation, for a hypersingular equation, and for a transmission problem.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1996-65-213/S0025-5718-96-00671-0/S0025-5718-96-00671-0.pdf

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