Adaptive FEM–BEM coupling with a Schur complement error indicator

In this paper an a-posteriori error estimate for non-linear coupled FEM–BEM equations is derived by using the Steklov–Poincaré operator and hierarchical basis techniques. We obtain “local” error indicators which are based on two-level subspace decompositions with the additive Schwarz operator. We present an algorithm for adaptive error control which is driven by these error indicators and numerical results are included.