2-LEVEL METHODS FOR THE SINGLE-LAYER POTENTIAL IN R-3

We consider weakly singular integral equations of the first kind on op en surface pieces Gamma in R-3. To obtain approximate solutions we use the h-version Galerkin boundary element method. Furthermore we introd uce two-level additive Schwarz operators for non-overlapping domain de compositions of Gamma and we estimate the conditions numbers of these operators with respect to the mesh size. Based on these operators we d erive an a posteriori error estimate for the difference between the ex act solution and the Galerkin solution. The estimate also involves the error which comes from an approximate solution of the Galerkin equati ons. For uniform meshes and under the assumption of a saturation condi tion we show reliability and efficiency of our estimate. Based on this estimate we introduce an adaptive multilevel algorithm with easily co mputable local error indicators which allows direction control of the local refinements. The theoretical results are illustrated by numerica l examples for plane and curved surfaces.