Publications in Scientific Journals:
M. Faustmann, J. Melenk, D. Praetorius:
"Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian";
Mathematics of Computation,
90
(2021),
1557
- 1587.
English abstract:
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.
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1090/mcom/3603
Created from the Publication Database of the Vienna University of Technology.