Talks and Poster Presentations (with Proceedings-Entry):

M. Feischl, T. Führer, M. Karkulik, J. Melenk, D. Praetorius:
"FEM-BEM couplings without stabilization (IABEM 2013)";
Talk: IABEM 2013 Symposium of the International Association for Boundary Element Methods, Santiago; 01-09-2012 - 01-11-2012; in: "IABEM 2013 Proceedings", Pontificia Universidad Católica de Chile, (2013), ISBN: 978-956-351-579-4; 48 - 53.

English abstract:
We consider a nonlinear interface problem which can equivalently be stated via various FEM-BEM coupling methods. We consider Costabelīs symmetric coupling as well as the non-symmetric Johnson-Nedelec coupling and the Bielak-MacCamy coupling. Due to constant functions in the kernel of these equations, these formulations are not elliptic and unique solvability cannot be shown directly.
We present a framework based on implicit theoretic stabilization to prove wellposedness of nonlinear FEM-BEM coupling formulations. We build on the works of Sayas and Steinbach and introduce stabilized coupling equations which are uniquely solvable and have the same solution as the (original) continuous resp. discrete coupling equations.
With this theoretic auxiliary problem, we obtain unique solvability of the original coupling equations. In particular, we avoid the solution of any additional equation and corresponding pre- and postprocessing steps as well as any assumption on the mesh-size.

FEM, BEM, coupling, nonlinearities, well-posedness

Electronic version of the publication:

Created from the Publication Database of the Vienna University of Technology.