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The Galerkin Finite Element Method for A Multi-term Time-Fractional Diffusion equation

Jin, B; Lazarov, R; Liu, Y; Zhou, Z; (2015) The Galerkin Finite Element Method for A Multi-term Time-Fractional Diffusion equation. Journal of Computational Physics , 281 pp. 825-843. 10.1016/j.jcp.2014.10.051. Green open access

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Abstract

We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite element method using continuous piecewise linear functions. Nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived, which cover both smooth and nonsmooth data. Further we develop a fully discrete scheme based on a finite difference discretization of the time-fractional derivatives, and discuss its stability and error estimate. Extensive numerical experiments for one and two-dimension problems confirm the theoretical convergence rates.

Type: Article
Title: The Galerkin Finite Element Method for A Multi-term Time-Fractional Diffusion equation
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.jcp.2014.10.051
Publisher version: http://dx.doi.org/10.1016/j.jcp.2014.10.051
Language: English
Additional information: This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Keywords: multi-term time-fractional diffusion equation, finite element method, error estimate, semidiscrete scheme, Caputo derivative
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/1453159
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