On the coupling of boundary integral and mixed finite element methods

We present a numerical method for solving an exterior Dirichlet problem in the plane. The technique consists in coupling boundary integral and mixed finite element methods. An artificial boundary is introduced separating an interior region from an exterior one. From an integral representation of the solution in the exterior domain we deduce two integral equations which relate the solution and its normal derivative over the artificial boundary. These integral equations are incorporated into the so-called mixed formulation of the problem in the interior region and a finite element method is used to approximate the resulting variational problem.