We analyze adaptive mesh-refining algorithms in the frame of boundary
element methods (BEM) and the coupling of finite elements and boundary
elements (FEM-BEM). Adaptivity is driven by the two-level error
estimator proposed by Ernst P. Stephan, Norbert Heuer, and coworkers in
the frame of BEM and FEM-BEM or by the residual error estimator introduced
by Birgit Faermann for BEM for weakly-singular integral equations. We prove that in either case
the usual adaptive algorithm drives the associated error estimator to
zero. Emphasis is put on the fact that the error estimators considered
are not even globally equivalent to weighted-residual error
estimators for which recently convergence with quasi-optimal algebraic rates has been derived.
CMAM considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. The journal is interdisciplinary while retaining the common thread of numerical analysis, readily readable and meant for a wide circle of researchers in applied mathematics.