An hp-adaptive refinement strategy for hypersingular operators on surfaces

Norbert Heuer
Numer. Methods Partial Differential Eq. 18 (3), 396-419, 2002.

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.