M. Faustmann, J. Melenk, D. Praetorius:

"Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian";

in: "ASC Report 07/2019", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2019, ISBN: 978-3-902627-12-4, 1 - 23.

For the discretization of the integral fractional Laplacian (-Laplace)^s, 0 < s < 1, based on piecewise linear functions, we present and analyze a reliable weighted residual a-posteriori error estimator. In order to compensate for a lack of L2-regularity of the

residual in the regime 3/4 < s < 1, this weighted residual error estimator includes as an additional weight a power of the distance from the mesh skeleton. We prove optimal convergence rates for an h-adaptive algorithm driven by this error estimator. Key to the

analysis of the adaptive algorithm are local inverse estimates for the fractional Laplacian.

http://www.asc.tuwien.ac.at/preprint/2019/asc07x2019.pdf

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