  We consider the convergence of adaptive BEM for weakly-singular and
hypersingular integral equations associated with the Laplacian and the
Helmholtz operator in 2D and 3D. The local mesh-refinement is driven by some
two-level error estimator. We show that the adaptive algorithm drives the
underlying error estimates to zero. Moreover, we prove that the saturation
assumption already implies linear convergence of the error with optimal
algebraic rates.
