A SEMIDISCRETE FINITE ELEMENT APPROXIMATION OF A TIME-FRACTIONAL FOKKER-PLANCK EQUATION WITH NONSMOOTH INITIAL DATA

被引：15

作者：

Le, Kim Ngan ^{[1
]}

McLean, William ^{[1
]}

Mustapha, Kassem ^{[2
]}

机构：

[1] Univ New South Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

[2] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2018年 / 40卷 / 06期

基金：

澳大利亚研究理事会;

关键词：

time-dependent forcing; stability; nonsmooth solutions; optimal convergence analysis; DISCONTINUOUS GALERKIN METHOD; DIFFERENCE-SCHEMES; COLLOCATION METHOD; DIFFUSION; FEM;

D O I：

10.1137/17M1125261

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：A3831 / A3852

页数：22

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