Adaptive coupling of FEM and BEM: Simple error estimators and convergence

A posteriori error estimators and adaptive mesh-refinement have themselves proven to be important tools for scientific computing. For error control in finite element methods (FEM), there is a broad variety of a posteriori error estimators available, and convergence as well as optimality of adaptive FEM is well-studied in the literature. This is, however, in sharp contrast to the boundary element method (BEM) and to the coupling of FEM and BEM. In our contribution, we present an easy-to-implement error estimator for some FEM-BEM coupling which, to the best of our knowledge, has not been proposed in the literature before. The derived mesh-refining algorithm provides the first adaptive coupling procedure which is mathematically proven to converge. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)