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-N\'ed\'elec 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 C\'ea-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 singularities.Comment: Published in Comput. Mech. online: Sep. 01, 201
