Talks and Poster Presentations (without Proceedings-Entry):
M. Aurada, M. Feischl, T. Führer, M. Karkulik, J. Melenk, D. Praetorius:
"Classical FEM-BEM couplings: well-posedness, nonlinearities, and adaptivity";
Talk: 8th Austrian Numerical Analysis Day,
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 Costabelīs 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.
Created from the Publication Database of the Vienna University of Technology.