ADAPTIVE BOUNDARY-ELEMENT METHODS FOR TRANSMISSION PROBLEMS

In this paper we present an adaptive boundary-element method for a tra nsmission problem for the Laplacian in a two-dimensional Lipschitz dom ain. We are concerned with an equivalent system of boundary-integral e quations of the first kind (on the transmission boundary) involving we akly-singular, singular and hypersingular integral operators. For the h-version boundary-element (Galerkin) discretization we derive an a po steriori error estimate which guarantees a given bound for the error i n the energy norm (up to a multiplicative constant). Then, following E riksson and Johnson this yields an adaptive algorithm steering the mes h refinement. Numerical examples confirm that our adaptive algorithms yield automatically good triangulations and are efficient.