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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

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