期刊
MATHEMATICS OF COMPUTATION
卷 90, 期 330, 页码 1557-1587出版社
AMER MATHEMATICAL SOC
DOI: 10.1090/mcom/3603
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资金
- Austrian Science Fund (FWF) by the special research program Taming complexity in PDE systems [SFB F65]
- FWF research project Optimal adaptivity for BEM [P27005]
This study introduces a reliable weighted residual a posteriori error estimator for the discretization of the integral fractional Laplacian, and proves optimal convergence rates for an h-adaptive algorithm driven by this error estimator. The key lies in the local inverse estimates for the fractional Laplacian, which are crucial for the analysis of the adaptive algorithm.
For the discretization of the integral fractional Laplacian (-Delta)(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 the lack of L-2-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.
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