Advances in Difference Equations | |
Superconvergence of a finite element method for the time-fractional diffusion equation with a time-space dependent diffusivity | |
article | |
An, Na1  | |
[1] School of Mathematics and Statistics, Shandong Normal University | |
关键词: Time-fractional diffusion; Caputo derivative; Finite element method; Superconvergence; | |
DOI : 10.1186/s13662-020-02976-4 | |
学科分类:航空航天科学 | |
来源: SpringerOpen | |
【 摘 要 】
In this work, a time-fractional diffusion problem with a time-space dependent diffusivity is considered. The solution of such a problem has a weak singularity at the initial time$t=0$ . Based on the L1 scheme in time on a graded mesh and the conforming finite element method in space on a uniform mesh, the fully discrete L1 conforming finite element method (L1 FEM) of a time-fractional diffusion problem is investigated. The error analysis is based on a nonstandard discrete Gronwall inequality. The final superconvergence result shows that an optimal grading of the temporal mesh should be selected as$r\geq (2-\alpha )/\alpha $ . Numerical results confirm that our analysis is sharp.
【 授权许可】
CC BY
【 预 览 】
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