A two-grid virtual element method for nonlinear variable-order time-fractional diffusion equation on polygonal meshes

被引：2
作者：
Gu, Qiling [1 ]
Chen, Yanping [2 ]
Zhou, Jianwei [3 ]
Huang, Yunqing [1 ]
机构：
[1] Xiangtan Univ, Sch Math & Computat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan, Peoples R China
[2] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Peoples R China
[3] Linyi Univ, Sch Math & Stat, Linyi, Peoples R China
来源：
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2023年 / 100卷 / 11期
基金：
中国国家自然科学基金;
关键词：
Virtual element method; nonlinear; variable-order fractional equation; two-grid; polygonal meshes; a priori error estimate; DISCRETIZATION;
D O I：
10.1080/00207160.2023.2263589
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we develop a two-grid virtual element method for nonlinear variable-order time-fractional diffusion equation on polygonal meshes. The L1 graded mesh scheme is considered in the time direction, and the VEM is used to approximate spatial direction. The two-grid virtual element algorithm reduces the solution of the nonlinear time fractional problem on a fine grid to one linear equation on the same fine grid and an original nonlinear problem on a much coarser grid. As a result, our algorithm not only saves total computational cost, but also maintains the optimal accuracy. Optimal L-2 error estimates are analysed in detail for both the VEM scheme and the corresponding two-grid VEM scheme. Finally, numerical experiments presented confirm the theoretical findings.
引用
收藏
页码：2124 / 2139
页数：16
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