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


Author: Carsten Carstensen
Journal: Math. Comp. 65 (1996), 69-84
MSC (1991): Primary 65N38, 65N15, 65R20, 45L10
DOI: https://doi.org/10.1090/S0025-5718-96-00671-0
MathSciNet review: 1320892
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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.


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Additional Information

Carsten Carstensen
Affiliation: Fachbereich Mathematik, Technische Hochschule Darmstadt, D 64283 Darmstadt, Germany
Email: carstensen@mathematik.th-darmstadt.de

DOI: https://doi.org/10.1090/S0025-5718-96-00671-0
Keywords: Boundary element method, a posteriori error estimate
Received by editor(s): March 22, 1994
Received by editor(s) in revised form: September 13, 1994
Article copyright: © Copyright 1996 American Mathematical Society