Journal article

A finite-volume scheme for fractional diffusion on bounded domains

Abstract:: We propose a new fractional Laplacian for bounded domains, expressed as a conservation law and thus particularly suited to finite-volume schemes. Our approach permits the direct prescription of no-flux boundary conditions. We first show the well-posedness theory for the fractional heat equation. We also develop a numerical scheme, which correctly captures the action of the fractional Laplacian and its anomalous diffusion effect. We benchmark numerical solutions for the Lévy–Fokker–Planck equation against known analytical solutions. We conclude by numerically exploring properties of these equations with respect to their stationary states and long-time asymptotics.

Publication status:: Published

Peer review status:: Peer reviewed

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APA Style

Bailo, R., Carrillo, J. A., Fronzoni, S., & Gómez-Castro, D. (2024). A finite-volume scheme for fractional diffusion on bounded domains. European Journal of Applied Mathematics, 36(2), 398–418.

MLA Style

Bailo, R., et al. “A Finite-Volume Scheme for Fractional Diffusion on Bounded Domains.” European Journal of Applied Mathematics, vol. 36, no. 2, Cambridge University Press, 2024, pp. 398–418.

Chicago Style

Bailo, R, JA Carrillo, S Fronzoni, and D Gómez-Castro. 2024. “A Finite-Volume Scheme for Fractional Diffusion on Bounded Domains.” European Journal of Applied Mathematics 36 (2): 398–418.
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Files:: Bailo_et_al_2024_A_finite-volume_scheme.pdf

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Publisher copy:: 10.1017/S0956792524000172

Authors

+ Bailo, R More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author

+ Carrillo, JA More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author
ORCID:: 0000-0001-8819-4660

+ Fronzoni, S More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author
ORCID:: 0000-0001-6300-8235

+ Gómez-Castro, D More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author

Publisher:: Cambridge University Press
Journal:: European Journal of Applied Mathematics More from this journal
Volume:: 36
Issue:: 2
Pages:: 398-418
Publication date:: 2024-04-16
Acceptance date:: 2024-03-23
DOI:: 10.1017/S0956792524000172
EISSN:: 1469-4425
ISSN:: 0956-7925

Language:: English
Keywords:: Levy-Fokker-Planck equation

fractional Laplacian

finite-volume schemes
Pubs id:: 1533172
Local pid:: pubs:1533172
Deposit date:: 2024-04-03

Terms of use

Copyright holder:: Bailo et al.
Copyright date:: 2024
Rights statement:: © The Author(s), 2024. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence, which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.

Licence:: CC Attribution (CC BY)

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