Coupling of mixed finite elements and boundary elements

The symmetric coupling of mixed finite element and boundary element methods is analysed for a model interface problem with the Laplacian. The coupling involves a further continuous ansatz function on the interface to link the discontinuous displacement field to the necessarily continuous boundary ansatz function. Quasi-optimal a priori error estimates and sharp a posteriori error estimates are established which justify adaptive mesh-refining algorithms. Numerical experiments prove the adaptive coupling as an efficient tool for the numerical treatment of transmission problems.