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

Mustapha, Kassem

doi:10.1090/mcom/3304

FEM for time-fractional diffusion equations, novel optimal error analyses
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Math. Comp. 87 (2018), 2259-2272 Request permission

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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