We analyze a multilevel diagonal additive Schwarz preconditioner for the adaptive coupling of FEM and BEM for a linear 2D Laplace transmission problem. We rigorously prove that the condition number of the preconditioned system stays uniformly bounded, independently of the refinement level and the local mesh-size of the underlying adaptively refined triangulations. Although the focus is on the non-symmetric Johnson-N\'ed\'elec one-equation coupling, the principle ideas also apply to other formulations like the symmetric FEM-BEM coupling. Numerical experiments underline our theoretical findings.
@article{arxiv.1311.5782,
title = {Optimal preconditioning for the symmetric and non-symmetric coupling of adaptive finite elements and boundary elements},
author = {Michael Feischl and Thomas Führer and Dirk Praetorius and Ernst P. Stephan},
journal= {arXiv preprint arXiv:1311.5782},
year = {2017}
}