A semidiscrete finite element approximation of a time-fractional Fokker-Planck equation with nonsmooth initial data
Numerical Analysis
2019-02-11 v1
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.
Keywords
Cite
@article{arxiv.1902.03204,
title = {A semidiscrete finite element approximation of a time-fractional Fokker-Planck equation with nonsmooth initial data},
author = {Kim Ngan Le and William McLean and Kassem Mustapha},
journal= {arXiv preprint arXiv:1902.03204},
year = {2019}
}