Author(s)

M.A. Golberg & H. Bowman

Abstract

We show for a variety of integral equations that the residual can be used as an error estimator provided that the Sloan iterate of the approximation supercon verges. This clarifies and generalizes a result given by Geng et al in [1]. When the solution technique is Galerkin's method, the superconvergence of the Sloan iterate can be established under quite general conditions, but is more difficult for collocation. We also show that it is important to consider the effect of numerical integration and other errors on these results as such errors can negate the superconvergence. 1 Introduction In recent years there has been considerable interest in the development of adaptive methods for solving boundary integral equations [1-4]. A key in- gredient in such algorithms

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