An a-posteriori error estimate for the coupling of BEM and mixed-FEM

We provide a reliable and computable a-posteriori error estimate for variational formulations arising from the coupling of boundary elements and mixed finite elements. As a model problem, we consider a linear second order elliptic equation in divergence form in a bounded annular region of the plane, coupled with Laplace equation in the surrounding unbounded exterior domain. Although we choose Raviart-Thomas elements, the a-posteriori estimate applies also to Brezzi-Douglas-Marini and Brezzi-Douglas-Fortin-Marini finite elements. In addition, we propose a strategy for solving the corresponding discrete problems, which is mainly based on a preconditioning technique for indefinite systems due to Bramble and Pasciak.

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