Reference : An a posteriori error estimator for the spectral fractional power of the Laplacian
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http://hdl.handle.net/10993/50748
An a posteriori error estimator for the spectral fractional power of the Laplacian
English
Bulle, Raphaël mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE) >]
Barrera, Olga []
Bordas, Stéphane mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE) >]
Chouly, Franz []
Hale, Jack mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE) >]
2022
Submitted pre-print
22
No
[en] Finite element methods ; A posteriori error estimation ; Fractional partial differential equations ; Adaptive refinement methods ; Bank–Weiser error estimator
[en] We develop a novel a posteriori error estimator for the L2 error committed by the finite ele- ment discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes advantage of the semi–discretization scheme using a rational approximation which allows to reformulate the fractional problem into a family of non–fractional parametric problems. The estimator involves applying the implicit Bank–Weiser error estimation strategy to each parametric non–fractional problem and reconstructing the fractional error through the same rational approximation used to compute the solution to the original fractional problem. We provide several numerical examples in both two and three-dimensions demonstrating the effectivity of our estimator for varying fractional powers and its ability to drive an adaptive mesh refinement strategy.
University of Luxembourg - UL
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http://hdl.handle.net/10993/50748
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
https://arxiv.org/abs/2202.05810
H2020 ; 811099 - DRIVEN - Increasing the scientific excellence and innovation capacity in Data-Driven Simulation of the University of Luxembourg

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