An hp-adaptive refinement strategy for hypersingular operators on surfaces

An adaptive refinement strategy for the hp-version of the boundary element method with hypersingular operators on surfaces is presented. The error indicators are based on local projections provided by two-level decompositions of ansatz spaces with additional bubble functions. Assuming a saturation property and locally quasi-uniform meshes, efficiency and reliability of the resulting error estimator is proved. A second error estimator based on mesh refinement and overlapping decompositions that better fulfills the saturation property is presented. The performance of the algorithm and the estimators is demonstrated for a model problem. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 396–419, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10011

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