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Spatial High Accuracy Analysis of FEM for Two-dimensional Multi-term Time-fractional Diffusion-wave Equations
Wei, Ya-bing1,2; Zhao, Yan-min1; Shi, Zheng-guang3; Wang, Fen-ling1; Tang, Yi-fa4,5
2018-10-01
Source PublicationACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
ISSN0168-9673
Volume34Issue:4Pages:828-841
AbstractIn this paper, high-order numerical analysis of finite element method (FEM) is presented for two-dimensional multi-term time-fractional diffusion-wave equation (TFDWE). First of all, a fully-discrete approximate scheme for multi-term TFDWE is established, which is based on bilinear FEM in spatial direction and Crank-Nicolson approximation in temporal direction, respectively. Then the proposed scheme is proved to be unconditionally stable and convergent. And then, rigorous proofs are given here for superclose properties in H-1-norm and temporal convergence in L-2-norm with order O(h(2) + tau(3-alpha)) where h and tau are the spatial size and time step, respectively. At the same time, theoretical analysis of global superconvergence in H-1-norm is derived by interpolation postprocessing technique. At last, numerical example is provided to demonstrate the theoretical analysis.
Keywordmulti-term time-fractional diffusion-wave equation bilinear finite element method Crank-Nicolson approximation stability convergence and superconvergence
DOI10.1007/s10255-018-0795-1
Language英语
Funding ProjectNational Natural Science Foundation of China[11771438] ; National Natural Science Foundation of China[11471296] ; Key Scientific Research Projects in Universities of Henan Province[19B110013] ; Program for Scientific and Technological Innovation Talents in Universities of Henan Province[19HASTIT025]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000446425100017
PublisherSPRINGER HEIDELBERG
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/31481
Collection计算数学与科学工程计算研究所
Affiliation1.Xuchang Univ, Sch Math & Stat, Xuchang 461000, Peoples R China
2.Beihang Univ, Sch Math & Syst Sci, Beijing 100191, Peoples R China
3.Southwestern Univ Finance & Econ, Sch Econ Math, Chengdu 611130, Sichuan, Peoples R China
4.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
5.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Wei, Ya-bing,Zhao, Yan-min,Shi, Zheng-guang,et al. Spatial High Accuracy Analysis of FEM for Two-dimensional Multi-term Time-fractional Diffusion-wave Equations[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,2018,34(4):828-841.
APA Wei, Ya-bing,Zhao, Yan-min,Shi, Zheng-guang,Wang, Fen-ling,&Tang, Yi-fa.(2018).Spatial High Accuracy Analysis of FEM for Two-dimensional Multi-term Time-fractional Diffusion-wave Equations.ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,34(4),828-841.
MLA Wei, Ya-bing,et al."Spatial High Accuracy Analysis of FEM for Two-dimensional Multi-term Time-fractional Diffusion-wave Equations".ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES 34.4(2018):828-841.
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