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FEM for time-fractional diffusion equations, novel optimal error analyses

Author: Kassem Mustapha
Journal: Math. Comp.
MSC (2010): Primary 65M12, 65M15, 65M60
Published electronically: January 24, 2018
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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.

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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

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.
Article copyright: © Copyright 2018 American Mathematical Society

American Mathematical Society