A weak Galerkin finite element approximation of two-dimensional sub-diffusion equation with time-fractional derivative

被引：4
|
作者：
Zhu, Ailing [1 ]
Wang, Yixin [1 ]
Xu, Qiang [1 ]
机构：
[1] Shandong Normal Univ, Sch Math & Stat, Jinan 250014, Shandong, Peoples R China
来源：
AIMS MATHEMATICS | 2020年 / 5卷 / 05期
关键词：
sub-diffusion equation; Caputo fractional derivative; weak Galerkin finite element method; discrete weak gradient; error estimate; DIFFERENCE SCHEME; ANOMALOUS DIFFUSION; ACCURACY; SUBDIFFUSION;
D O I：
10.3934/math.2020274
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We develop a fully discrete weak Galerkin finite element method for the initial-boundary value problem of two-dimensional sub-diffusion equation with Caputo time-fractional derivative. A traditional L-1 discretization for the Caputo time-fractional derivative and a weak Galerkin scheme for the space integer differential operator are employed. We prove the stability of the numerical method and establish the error estimate in L-2 and discrete H-1 norms, respectively. Some numerical results are reported to confirm the theory.
引用
收藏
页码：4297 / 4310
页数：14
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