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A posteriori error estimates for boundary element methods


Authors: Carsten Carstensen and Ernst P. Stephan
Journal: Math. Comp. 64 (1995), 483-500
MSC: Primary 65N38
DOI: https://doi.org/10.1090/S0025-5718-1995-1277764-7
MathSciNet review: 1277764
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Abstract: This paper deals with a general framework for a posteriori error estimates in boundary element methods which is specified for three examples, namely Symm's integral equation, an integral equation with a hypersingular operator, and a boundary integral equation for a transmission problem. Based on these estimates, an analog of Eriksson and Johnson's adaptive finite element method is proposed for the h-version of the Galerkin boundary element method for integral equations of the first kind. The efficiency of the approach is shown by numerical experiments which yield almost optimal convergence rates even in the presence of singularities.


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DOI: https://doi.org/10.1090/S0025-5718-1995-1277764-7
Keywords: A posteriori error estimates, boundary element methods, adaptive boundary element methods
Article copyright: © Copyright 1995 American Mathematical Society