R.M. Correa
The solution of the anomalous diffusion equation by a Finite Element Method based on the Caputo derivative
Correa, R.M.; Carrer, J.A.M.; Solheid, B.S.; Trevelyan, J.
Abstract
A Finite Element Method formulation is developed for the solution of the anomalous diffusion equation. This equation belongs to the branch of mathematics called fractional calculus; it is governed by a partial differential equation in which a fractional time derivative, whose order ranges in the interval (0,1), replaces the first order time derivative of the classical diffusion equation. In this work, the Caputo integro-differential operator is employed to represent the fractional time derivative. After assuming a linear time variation for the variable of interest, say u, in the intervals in which the overall time is discretized, the integral in the Caputo operator is computed analytically. To demonstrate the usefulness of the proposed formulation, some examples are analysed, showing a good agreement between the FEM results the analytical solutions, even for small orders of the time derivative.
Citation
Correa, R., Carrer, J., Solheid, B., & Trevelyan, J. (2022). The solution of the anomalous diffusion equation by a Finite Element Method based on the Caputo derivative. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 44(6), Article 250. https://doi.org/10.1007/s40430-022-03544-5
Journal Article Type | Article |
---|---|
Acceptance Date | Apr 19, 2022 |
Online Publication Date | May 27, 2022 |
Publication Date | 2022-06 |
Deposit Date | May 11, 2022 |
Publicly Available Date | May 27, 2023 |
Journal | Journal of the Brazilian Society of Mechanical Sciences and Engineering |
Print ISSN | 1678-5878 |
Electronic ISSN | 1806-3691 |
Publisher | Springer Berlin Heidelberg |
Peer Reviewed | Peer Reviewed |
Volume | 44 |
Issue | 6 |
Article Number | 250 |
DOI | https://doi.org/10.1007/s40430-022-03544-5 |
Public URL | https://durham-repository.worktribe.com/output/1206385 |
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Copyright Statement
The version of record of this article, first published in Journal of the Brazilian Society of Mechanical Sciences and Engineering, is available online at Publisher’s website: http://dx.doi.org/10.1007/s40430-022-03544-5
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