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Article Dans Une Revue Computer Methods in Applied Mechanics and Engineering Année : 2023

An a posteriori error estimator for the spectral fractional power of the Laplacian

Résumé

We develop a novel a posteriori error estimator for the L2 error committed by the finite element 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.
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Dates et versions

hal-03567028 , version 1 (11-02-2022)

Identifiants

Citer

Raphaël Bulle, Olga Barrera, Stéphane P.A. Bordas, Franz Chouly, Jack S Hale. An a posteriori error estimator for the spectral fractional power of the Laplacian. Computer Methods in Applied Mechanics and Engineering, 2023, 407, pp.115943. ⟨10.1016/j.cma.2023.115943⟩. ⟨hal-03567028⟩
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