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Efficiency of a posteriori BEM--error estimates for first-kind integral equations on quasi--uniform meshes
Author(s):
Carsten
Carstensen.
Journal:
Math. Comp.
65
(1996),
69-84.
MSC (1991):
Primary 65N38, 65N15, 65R20, 45L10
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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:
10.1090/S0025-5718-96-00671-0
PII:
S 0025-5718(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.
Copyright of article:
Copyright
1996,
American Mathematical Society
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