A new numerical method on linear exterior boundary value problem in R 2

In this paper, based on the boundary reduction advanced by Han, we present a new method for solving an exterior Dirichlet problem in the plane. The technique consists in coupling the boundary element with the mixed finite element method. An artifical boundary is introduced separating an interior region from an exterior one. From the theory of the boundary element in the exterior domain we deduce the connection which relates the solution and its normal derivative over the artificial boundary. These results are incorporated into the so-called mixed formulation of the problem in the interior region.