Finite element methods; A posteriori error estimation; Fractional partial differential equations; Adaptive refinement methods; Bank–Weiser error estimator
Abstract :
[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.
Research center :
ULHPC - University of Luxembourg: High Performance Computing
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others Mathematics
Author, co-author :
BULLE, Raphaël ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE)
Barrera, Olga
BORDAS, Stéphane ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE)
Chouly, Franz
HALE, Jack ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE)
External co-authors :
yes
Language :
English
Title :
An a posteriori error estimator for the spectral fractional power of the Laplacian
Publication date :
2023
Journal title :
Computer Methods in Applied Mechanics and Engineering
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