Space-time finite element method for the multi-term time-space fractional diffusion equation on a two-dimensional domain

被引：35

作者：

Bu, Weiping ^{[1
,2
]}

Shu, Shi ^{[1
,2
]}

Yue, Xiaoqiang ^{[1
,2
]}

Xiao, Aiguo ^{[1
,2
]}

Zeng, Wei ^{[1
,2
]}

机构：

[1] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

[2] Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2019年 / 78卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Multi-term time-space fractional diffusion equation; Space-time finite element method; Wellposedness; Graded mesh; Error estimates; ANOMALOUS DIFFUSION; SCHEME;

D O I：

10.1016/j.camwa.2018.11.033

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose a space-time finite element method for the multi-term time-space fractional diffusion equation. First, some fractional derivative spaces are listed, some properties of the fractional derivatives and fractional derivative spaces are given, some definitions and properties of finite element spaces are introduced, and a space-time finite element fully discrete scheme for the considered problem is developed. Second, the existence, uniqueness and stability of the obtained numerical scheme are discussed. Third, under the hypothesis about singular behavior of exact solution near t = 0, the convergence is investigated in detail based on the suitable graded time mesh. At last, some numerical tests are given to verify the rationality and effectiveness of our method. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：1367 / 1379

页数：13

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