ADAPTIVE BOUNDARY-ELEMENT METHODS FOR SOME FIRST KIND INTEGRAL-EQUATIONS

In this paper we present an adaptive boundary element method for the b oundary integral equations of the first kind concerning the Dirichlet problem and the Neumann problem for the Laplacian in a two-dimensional Lipschitz domain. For the h-version of the finite element Galerkin di scretization of the single layer potential and the hypersingular opera tor, we derive a posteriori error estimates which guarantee a given bo und for the error in the energy norm (up to a multiplicative constant) . Following Eriksson and Johnson this yields adaptive algorithms steer ing the mesh refinement. Numerical examples confirm that our adaptive algorithms yield automatically the expected convergence rate.