M. Aurada, M. Feischl, T. Führer, M. Karkulik, J. Melenk, D. Praetorius:
"Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity";
Computational Mechanics, 51 (2013), 4; S. 399 - 419.

Kurzfassung englisch:
We consider a (possibly) nonlinear interface problem in 2D and 3D,
which is solved by use of various adaptive FEM-BEM coupling
strategies, namely 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. For the respective Galerkin discretizations with lowest-order
polynomials, we provide reliable residual-based error estimators.
Together with an estimator reduction property, we prove convergence
of the adaptive FEM-BEM coupling methods. A key point for the proof
of the estimator reduction are novel inverse-type estimates for the
involved boundary integral operators which are advertized. Numerical
experiments conclude the work and compare performance and effectivity
of the three adaptive coupling procedures in the presence of generic

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