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High-accuracy finite element method for 2D time fractional diffusion-wave equation on anisotropic meshes
Zhang, Y. D.1; Zhao, Y. M.1; Wang, F. L.1; Tang, Y. F.2,3
2018
Source PublicationINTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
ISSN0020-7160
Volume95Issue:1Pages:218-230
AbstractEmploying finite element method in spatial direction and Crank-Nicolson scheme in temporal direction, a fully discrete scheme with high accuracy is established for a class of two-dimensional time fractional diffusion-wave equation with Caputo fractional derivative. Unconditional stability analysis of the approximate scheme is proposed. The spatial global superconvergence and temporal convergence of order O(h(2) + tau(3-alpha)) for the original variable in H-1-norm is presented by means of properties of bilinear element and interpolation postprocessing technique without Ritz projection, where h and tau are the step sizes in space and time, respectively. Finally, several numerical results are implemented to evaluate the efficiency of the theoretical results on both regular and anisotropic meshes.
KeywordTime fractional diffusion-wave equation finite element method Crank-Nicolson scheme stability convergence and superconvergence
DOI10.1080/00207160.2017.1401708
Language英语
Funding ProjectNational Natural Science Foundation of China[11101381] ; National Natural Science Foundation of China[11771438] ; Outstanding Young Talents Training Plan by Xuchang University
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000428749300014
PublisherTAYLOR & FRANCIS LTD
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/30058
Collection中国科学院数学与系统科学研究院
Corresponding AuthorZhao, Y. M.
Affiliation1.Xuchang Univ, Sch Math & Stat, Xuchang, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Zhang, Y. D.,Zhao, Y. M.,Wang, F. L.,et al. High-accuracy finite element method for 2D time fractional diffusion-wave equation on anisotropic meshes[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,2018,95(1):218-230.
APA Zhang, Y. D.,Zhao, Y. M.,Wang, F. L.,&Tang, Y. F..(2018).High-accuracy finite element method for 2D time fractional diffusion-wave equation on anisotropic meshes.INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,95(1),218-230.
MLA Zhang, Y. D.,et al."High-accuracy finite element method for 2D time fractional diffusion-wave equation on anisotropic meshes".INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 95.1(2018):218-230.
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