Optimal preconditioning for the symmetric and nonsymmetric coupling of adaptive finite elements and boundary elements



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 nonsymmetric Johnson–Nédélec one-equation coupling, the principle ideas also apply to other formulations like the symmetric FEM-BEM coupling. Numerical experiments underline our theoretical findings. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 603–632, 2017