Improving the convergence of some boundary element methods

Abstract

We will discuss three possibilities of how to improve the approximation quality of boundary element approximations for integral equations of the first kind on smooth planar curves. First we comment on iterated finite element solutions, then on reduced integration techniques resulting in so-called qualocation methods. As a third option we present post-processing based on a recent superconvergence result of the author. For this last approach we present numerical experiments in the context of adaptive refinement.