The saturation assumption yields optimal convergence of two-level adaptive BEM

Quasi-Optimal Adaptive BEM

Estimator reduction and convergence of adaptive BEM

A posteriori error estimation and related adaptive mesh-refining algorithms have themselves proven to be powerful tools in nowadays scientific computing. Contrary to adaptive finite element methods, convergence of adaptive boundary element schemes is, however, widely open. We propose a relaxed notion of convergence of adaptive boundary element schemes. Instead of asking for convergence of the e...

Convergence of Adaptive BEM and Adaptive FEM-BEM Coupling for Estimators Without h-Weighting Factor

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-singula...

Justification of the saturation assumption

The saturation assumption is widely used in computational science and engineering, usually without any rigorous theoretical justification and even despite of counterexamples for some coarse meshes known in the mathematical literature. On the other hand, there is overwhelming numerical evidence at least in an asymptotic regime for the validity of the saturation. In the generalized form, the assu...

Simultaneous quasi-optimal convergence in FEM-BEM coupling

On linear ODEs with a time singularity of the rst kind and unsmooth inhomo-geneity 6/2014 A degenerate fourth-order parabolic equation modeling Bose-Einstein condensation. We consider the symmetric FEM-BEM coupling that connects two linear elliptic second order partial differential equations posed in a bounded domain Ω and its complement, where the exterior problem is restated by an integral eq...