KMS Of Academy of mathematics and systems sciences, CAS
| Galerkin finite element method for two-dimensional space and time fractional Bloch-Torrey equation | |
Zhao, Yue1; Bu, Weiping2; Zhao, Xuan3; Tang, Yifa1,4
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| 2017-12-01 | |
| Source Publication | JOURNAL OF COMPUTATIONAL PHYSICS
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| ISSN | 0021-9991 |
| Volume | 350Pages:117-135 |
| Abstract | 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. |
| Keyword | Space and time fractional Bloch-Torrey equation Galerkin finite element method L2-1(sigma) formula Stability Convergence |
| DOI | 10.1016/j.jcp.2017.08.051 |
| Language | 英语 |
| Funding Project | 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 Research Area | Computer Science ; Physics |
| WOS Subject | Computer Science, Interdisciplinary Applications ; Physics, Mathematical |
| WOS ID | WOS:000413379000007 |
| Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/26785 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Zhao, Yue |
| Affiliation | 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 |
| Recommended Citation 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. |
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