FEM for time-fractional diffusion equations, novel optimal error analyses
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Abstract:
A semidiscrete Galerkin finite element method applied to time-fractional diffusion equations with time-space dependent diffusivity on bounded convex spatial domains will be studied. The main focus is on achieving optimal error results with respect to both the convergence order of the approximate solution and the regularity of the initial data. By using novel energy arguments, for each fixed time $t$, optimal error bounds in the spatial $L^2$- and $H^1$-norms are derived for both cases: smooth and nonsmooth initial data. Some numerical results will be provided at the end.References
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Additional Information
- Kassem Mustapha
- Affiliation: Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia
- MR Author ID: 727133
- Email: kassem@kfupm.edu.sa
- Received by editor(s): October 5, 2016
- Received by editor(s) in revised form: March 15, 2017, and May 3, 2017
- Published electronically: January 24, 2018
- Additional Notes: The support of KFUPM through project No. FT151002 is gratefully acknowledged.
- © Copyright 2018 American Mathematical Society
- Journal: Math. Comp. 87 (2018), 2259-2272
- MSC (2010): Primary 65M12, 65M15, 65M60
- DOI: https://doi.org/10.1090/mcom/3304
- MathSciNet review: 3802434