A posteriori error estimates for the Johnson–Nédélec FEM–BEM coupling

Only very recently, Sayas [The validity of Johnson–Nédélecʹs BEM-FEM coupling on polygonal interfaces. SIAM J Numer Anal 2009;47:3451–63] proved that the Johnson–Nédélec one-equation approach from [On the coupling of boundary integral and finite element methods. Math Comput 1980;35:1063–79] provides a stable coupling of finite element method (FEM) and boundary element method (BEM). In our work, we now adapt the analytical results for different a posteriori error estimates developed for the symmetric FEM–BEM coupling to the Johnson–Nédélec coupling. More precisely, we analyze the weighted-residual error estimator, the two-level error estimator, and different versions of (h−h/2)-based error estimators. In numerical experiments, we use these estimators to steer h-adaptive algorithms, and compare the effectivity of the different approaches.