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We consider the convergence of adaptive BEM for weakly-singular andhypersingular integral equations associated with the Laplacian and theHelmholtz operator in 2D and 3D. The local mesh-refinement is driven by sometwo-level error estimator. We show that the adaptive algorithm drives theunderlying error estimates to zero. Moreover, we prove that the saturationassumption already implies linear convergence of the error with optimalalgebraic rates.

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