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arXiv · 1902.03204

A semidiscrete finite element approximation of a time-fractional Fokker-Planck equation with nonsmooth initial data

Kim Ngan Le·William McLean·Kassem Mustapha
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Abstract

We present a new stability and convergence analysis for the spatial discretization of a time-fractional Fokker--Planck equation in a convex polyhedral domain, using continuous, piecewise-linear, finite elements. The forcing may depend on time as well as on the spatial variables, and the initial data may have low regularity. Our analysis uses a novel sequence of energy arguments in combination with a generalized Gronwall inequality. Although this theory covers only the spatial discretization, we present numerical experiments with a fully discrete scheme employing a very small time step, and observe results consistent with the predicted convergence behavior.

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Kim Ngan Le, William McLean, Kassem Mustapha. 2019-02-08. A semidiscrete finite element approximation of a time-fractional Fokker-Planck equation with nonsmooth initial data. https://doi.org/10.1137/17m1125261

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