Galerkin finite element method for two-dimensional space and time fractional Bloch-Torrey equation
文献类型：期刊论文
| 作者 | Zhao, Yue1; Bu, Weiping2; Zhao, Xuan3; Tang, Yifa1,4
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| 刊名 | JOURNAL OF COMPUTATIONAL PHYSICS
 |
| 出版日期 | 2017-12-01 |
| 卷号 | 350页码:117-135 |
| 关键词 | Space and time fractional Bloch-Torrey equation Galerkin finite element method L2-1(sigma) formula Stability Convergence |
| ISSN号 | 0021-9991 |
| DOI | 10.1016/j.jcp.2017.08.051 |
| 英文摘要 | In this paper, we consider the Galerkin finite element method for the two-dimensional space and time fractional Bloch-Torrey equation (2D-STFBTE). Utilizing the L2-1 sigma formula to discretize temporal Caputo derivative, we obtain the local truncation error with O (iota H3-Q) in the temporal direction, where a is the order of time fractional derivative. Furthermore, the semi-discrete form for the problem is given and, the stability and convergence of the semi-discrete variational formulation are rigorously proved in L-2 norm and fractional norm respectively. Then, we derive a fully discrete scheme for the 2D-STFBTE and investigate its convergence theoretically. Finally, extensive numerical results based on linear piecewise polynomials verify the theoretical results and show the effectiveness of the proposed scheme. (C) 2017 Elsevier Inc. All rights reserved. |
| 资助项目 | State Key Program of National Natural Science Foundation of China[11631013] ; National Natural Science Foundation of China[11371357] ; National Natural Science Foundation of China[11601460] ; Research Foundation of Education Commission of Hunan Province of China[1601540] ; ITER-China Program[2014GB124005] |
| WOS研究方向 | Computer Science ; Physics |
| 语种 | 英语 |
| WOS记录号 | WOS:000413379000007 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/26784]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Zhao, Yue |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China 3.Southeast Univ, Sch Math, Nanjing 210096, Jiangsu, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
| 推荐引用方式 GB/T 7714 | Zhao, Yue,Bu, Weiping,Zhao, Xuan,et al. Galerkin finite element method for two-dimensional space and time fractional Bloch-Torrey equation[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2017,350:117-135. |
| APA | Zhao, Yue,Bu, Weiping,Zhao, Xuan,&Tang, Yifa.(2017).Galerkin finite element method for two-dimensional space and time fractional Bloch-Torrey equation.JOURNAL OF COMPUTATIONAL PHYSICS,350,117-135. |
| MLA | Zhao, Yue,et al."Galerkin finite element method for two-dimensional space and time fractional Bloch-Torrey equation".JOURNAL OF COMPUTATIONAL PHYSICS 350(2017):117-135. |
入库方式： OAI收割
来源：数学与系统科学研究院
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