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A novel high-order approximate scheme for two-dimensional time-fractional diffusion equations with variable coefficient
Wang, Fenling1; Zhao, Yanmin1; Chen, Chen2; Wei, Yabing3; Tang, Yifa2,4
2019-09-01
发表期刊COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN0898-1221
卷号78期号:5页码:1288-1301
摘要Based on the spatial quasi-Wilson nonconforming finite element method and temporal L2 - 1(sigma) , formula, a fully-discrete approximate scheme is proposed for a two-dimensional time-fractional diffusion equations with variable coefficient on anisotropic meshes. In order to demonstrate the stable analysis and error estimates, several lemmas are provided, which focus on high accuracy about projection and superclose estimate between the interpolation and projection. Unconditionally stable analysis are derived in L-2-norm and broken H-1-norm. Moreover, convergence result of accuracy O(h(2) + tau(2)) and superclose property of accuracy O(h(2) + tau(2)) are deduced by combining interpolation with projection, where h and tau are the step sizes in space and time, respectively. And then, the global superconvergence is presented by employing interpolation post processing operator. Finally, numerical results are provided to demonstrate the validity of the theoretical analysis. (C) 2018 Elsevier Ltd. All rights reserved.
关键词Time-fractional diffusion equations Variable coefficient Quasi-Wilson nonconforming anisotropic finite element L2-1(sigma) formula Stability Superclose and superconvergence
DOI10.1016/j.camwa.2018.11.029
语种英语
资助项目National Natural Science Foundation of China[11771438] ; National Natural Science Foundation of China[11471296] ; Key Scientific Research Projects in Universities of Henan Province, China[198110013] ; Program for Scientific and Technological Innovation Talents in Universities of Henan Province, China[19HASTIT025]
WOS研究方向Mathematics
WOS类目Mathematics, Applied
WOS记录号WOS:000482248100005
出版者PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型期刊论文
条目标识符http://ir.amss.ac.cn/handle/2S8OKBNM/35478
专题计算数学与科学工程计算研究所
通讯作者Zhao, Yanmin; Tang, Yifa
作者单位1.Xuchang Univ, Sch Math & Stat, Xuchang 461000, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
3.Beihang Univ, Sch Math & Syst Sci, Beijing 100191, Peoples R China
4.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China
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Wang, Fenling,Zhao, Yanmin,Chen, Chen,et al. A novel high-order approximate scheme for two-dimensional time-fractional diffusion equations with variable coefficient[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2019,78(5):1288-1301.
APA Wang, Fenling,Zhao, Yanmin,Chen, Chen,Wei, Yabing,&Tang, Yifa.(2019).A novel high-order approximate scheme for two-dimensional time-fractional diffusion equations with variable coefficient.COMPUTERS & MATHEMATICS WITH APPLICATIONS,78(5),1288-1301.
MLA Wang, Fenling,et al."A novel high-order approximate scheme for two-dimensional time-fractional diffusion equations with variable coefficient".COMPUTERS & MATHEMATICS WITH APPLICATIONS 78.5(2019):1288-1301.
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