Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 27, Issue 4, Pages 1226-1260Publisher
SIAM PUBLICATIONS
DOI: 10.1137/040609033
Keywords
integral equations; boundary element method; a posteriori error estimates; reliability; efficiency; adaptive algorithm
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Averaging techniques for finite element error control, occasionally called ZZ estimators for the gradient recovery, enjoy a high popularity in engineering because of their striking simplicity and universality: One does not even require a PDE to apply the nonexpensive post-processing routines. Recently, averaging techniques have been mathematically proved to be reliable and efficient for various applications of the finite element method. This paper establishes a class of averaging error estimators for boundary integral methods. Symm's integral equation of the first kind with a nonlocal single-layer integral operator serves as a model equation studied both theoretically and numerically. We introduce four new error estimators which are proven to be reliable and efficient up to terms of higher order. The higher-order terms depend on the regularity of the exact solution. Several numerical experiments illustrate the theoretical results and show that the [ normally unknown] error is sharply estimated by the proposed estimators, i.e., error and estimators almost coincide.
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