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M. Aurada, M. Feischl, T. Führer, M. Karkulik, J. Melenk, D. Praetorius:
"Classical FEM-BEM couplings: well-posedness, nonlinearities, and adaptivity";
Vortrag: 8th Austrian Numerical Analysis Day, Wien; 10.05.2012 - 11.05.2012.

We consider a (possibly) nonlinear interface problem in 2D or 3D, which can be solved by the use of different FEM-BEM coupling methods. In particular, we consider the Johnson-Nedelec coupling, the Bielak-MacCamy coupling and Costabel´s symmetric coupling. We provide a framework to prove that the continuous as well as the discrete Galerkin solutions of these coupling methods additionally solve an appropriate operator equation with a Lipschitz continuous and strongly monotone operator. Therefore, the coupling formulations are well-defined, and the Galerkin solutions are quasi-optimal in the sense of a Cea-type lemma.

Moreover, we provide reliable residual-based error estimators for the Galerkin discretization with lowest-order polynomials. Together with an estimator reduction property, we prove convergence of the adaptive FEM-BEM coupling methods. The key ingredient are novel inverse-type estimates for the boundary integral operators involved.