Galerkin collocation for an improved boundary element method for a plane mixed boundary value problem

We present the numerical implementation of a boundary element approximation for the plane mixed boundary value problem of the Laplacian. The performed Galerkin procedure is based on the direct boundary integral method. Its accuracy is improved by using appropriate singularity functions as additional test and trial functions besides quadratic splines. We analize the consistency error of the used numerical integrations and present asymptotic error estimates for the fully discretized numerical scheme which are of the same optimal orders as the Galerkin errors.