Only very recently, Sayas [The validity of JohnsonNédélecs BEM-FEM coupling on polygonal interfaces. SIAM J Numer Anal 2009;47:345163] proved that the JohnsonNédélec one-equation approach from [On the coupling of boundary integral and finite element methods. Math Comput 1980;35:106379] 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 FEMBEM coupling to the JohnsonNédélec 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. © 2011 Elsevier Ltd. All rights reserved.
Aurada, M., Feischl, M., Karkulik, M., & Praetorius, D. (2012). A posteriori error estimates for the JohnsonNédélec FEMBEM coupling. Engineering Analysis with Boundary Elements, 255-266. https://doi.org/10.1016/j.enganabound.2011.07.017