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

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

ISSN :

1879-2138

Publisher :

Elsevier, Amsterdam, Netherlands

Volume :

407

Pages :

115943

Peer reviewed :

Peer reviewed

Focus Area :

Computational Sciences

Additional URL :

https://arxiv.org/abs/2202.05810

European Projects :

H2020 - 811099 - DRIVEN - Increasing the scientific excellence and innovation capacity in Data-Driven Simulation of the University of Luxembourg

Name of the research project :

ASSIST

Funders :

University of Luxembourg - UL
CE - Commission Européenne [BE]

Available on ORBilu :

since 03 April 2022

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