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.
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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-pp.ucl.ac.uk/id/eprint/1453159 |
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