On the numerical solution of linear exterior problems via the uncoupling method

The application of the uncoupling of boundary integral and Þnite element methods to solve exterior boundary value problems in R2 yields a weak formulation that contains only one boundary term. This is the so-called uncoupling term, which is determined by the boundary integral operator of the single-layer potential acting on a circle centered at the origin. The purpose of this paper is to provide a suitable formula, which combines analytical and numerical methods, to approximately integrate the uncoupling term to any exacteness. Our method provides sharper error estimates than the one that uses Truncated InÞnite Fourier Series (TIFE). As a model we consider the exterior Dirichlet problem for the Laplacian, and use linear Þnite elements for the corresponding Galerkin scheme. Some numerical experiments are also presented