In this paper we combine the dual-mixed finite element method with a Dirichlet-to-Neumann mapping(given in terms of a boundary integral operator) to solve linear exterior transmission problems inthe plane. As a model we consider a second order elliptic equation in divergence form coupled withthe Laplace equation in the exterior unbounded region. We show that the resulting mixed variationalformulation and an associated discrete scheme using Raviart-Thomas spaces are well posed, and derivethe usual Cea error estimate and the corresponding rate of convergence. In addition, we develop twodifferent a-posteriori error analyses yielding explicit residual and implicit Bank-Weiser typereliable estimates, respectively. Several numerical results illustrate the suitability of theseestimators for the adaptive computation of the discrete solutions.
