Coupling of FEM and BEM for a transmission problem with nonlinear interface conditions. Hierarchical and residual error indicators

In this paper we consider the coupling of finite elements and boundary elements for a transmission problem with a nonlinear transmission condition. We first consider the uniform h-version and show how to linearise the resulting systems by Newtonʼs method. Next we derive a posteriori error estimates of hierarchical and residual type and implement corresponding adaptive procedures. Our results show that for the nonlinear transmission problem optimal mesh refinements are obtained with our error controlled approach.