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 an
satz function. Quasi-optimal a priori error estimates and sharp a posterior
i error estimates are established which justify adaptive mesh-refining algo
rithms. Numerical experiments prove the adaptive coupling as an efficient t
ool for the numerical treatment of transmission problems.