Contributions to Books:
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,
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.
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.