Coupling of mixed finite elements and boundary elements

The symmetric coupling of mixed finite element and boundaryelement methods is analysed for a model interface problem withthe Laplacian. The coupling involves a further continuous ansatzfunction on the interface to link the discontinuous displacementfield to the necessarily continuous boundary ansatz function.Quasi-optimal a priori error estimates and sharp a posteriorierror estimates are established which justify adaptive mesh-refiningalgorithms. Numerical experiments prove the adaptive couplingas an efficient tool for the numerical treatment of transmissionproblems.