publication . Article . Preprint . 2016

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

Kassem Mustapha;
Open Access
  • Published: 18 Oct 2016 Journal: Mathematics of Computation, volume 87, pages 2,259-2,272 (issn: 0025-5718, eissn: 1088-6842, Copyright policy)
  • Publisher: American Mathematical Society (AMS)
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.
Persistent Identifiers
Subjects
free text keywords: Algebra and Number Theory, Applied Mathematics, Computational Mathematics, Mathematics - Numerical Analysis, Finite element method, Fractional diffusion, Mathematical analysis, Mathematics
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