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The solution of the anomalous diffusion equation by a Finite Element Method based on the Caputo derivative

Correa, R.M. and Carrer, J.A.M. and Solheid, B.S. and 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). p. 250.

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.

Item Type:Article
Full text:Publisher-imposed embargo until 27 May 2023.
(AM) Accepted Manuscript
File format - PDF
(2462Kb)
Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/s40430-022-03544-5
Publisher 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
Date accepted:19 April 2022
Date deposited:12 May 2022
Date of first online publication:27 May 2022
Date first made open access:27 May 2023

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