A finite element approximation for a class of Caputo time-fractional diffusion equations

We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates are derived. The accuracy and efficiency of the presented me...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2019-09, Vol.78 (5), p.1334-1344
Main Authors: Sidi Ammi, Moulay Rchid, Jamiai, Ismail, Torres, Delfim F.M.
Format: Article
Language:English
Subjects:
Error detection
Finite difference method
Finite element method
Fractional partial differential equations
Mathematical analysis
Nonlinear programming
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Summary:We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates are derived. The accuracy and efficiency of the presented method is shown by conducting two numerical examples.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2019.05.031