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

Praetorius, Dirk and Ruggeri, Michele and Stephan, Ernst P. (2020) The saturation assumption yields optimal convergence of two-level adaptive BEM. Applied Numerical Mathematics, 152. pp. 105-124. ISSN 0168-9274 (https://doi.org/10.1016/j.apnum.2020.01.014)

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Abstract

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.

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