Superconvergence and the use of the residual as an error estimator in the BEM. II: Collocation, numerical integration and error indicators

We show for a variety of integral equations that the residual can be used a s an error estimator provided the Sloan iterate of the approximation superc onverges. This generalizes a result given by Geng el al. [J. Acoust. Soc. A m. 100 (1996) 355]. When the solution technique is Galerkin's method we sho w that the superconvergence of the Sloan iterate can be established under q uite general conditions. For collocation this is more difficult and we disc uss a generalization of a result of Brunner [J. Comp. Appl. Math. 67 (1996) 185] for doing this. Using ideas of Schulz [Uher lokale and globale Fehler gsehatzungen fur adaptive randelment Methoden, PhD thesis, Mathematisches I nstitute A, University of Stuttgart, 1997] it is shown how to localize thes e results to provide asymptotically exact local error indicators. It is als o shown that it is important to consider the effect of numerical integratio n errors. as such errors can destroy superconvergence. (C) 2001 Elsevier Sc ience Ltd. All rights reserved.