We prove convergence and quasi-optimality of a lowest-order adaptive
boundary element method for a weakly-singular integral equation in 2D.
The adaptive mesh-refinement is driven by the weighted-residual
error estimator. By proving that this estimator is not only reliable, but under some
regularity assumptions on the given data also efficient on locally refined meshes, we characterize the approximation class in terms of the Galerkin error only.
In particular, this yields that no
adaptive strategy can do better, and the weighted-residual error estimator is thus an optimal choice to steer the adaptive mesh-refinement. As a side result, we prove a
weak form of the saturation assumption.
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