Anisotropic linear triangle finite element approximation for multi-term time-fractional mixed diffusion and diffusion-wave equations with variable coefficient on 2D bounded domain

doi:10.1016/j.camwa.2018.11.028

	Anisotropic linear triangle finite element approximation for multi-term time-fractional mixed diffusion and diffusion-wave equations with variable coefficient on 2D bounded domain
	Zhao, Yanmin 1; Wang, Fenling 1; Hu, Xiaohan 2; Shi, Zhengguang 3; Tang, Yifa2,4
	2019-09-01
发表期刊	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
卷号	78 期号:5 页码:1705-1719
摘要	A fully-discrete approximate scheme is established for the 2D multi-term time-fractional mixed diffusion and diffusion-wave equations with spatial variable coefficient by using linear triangle finite element method in space and classical L1 time-stepping method combined with Crank-Nicolson scheme in time. Then, the unconditionally stable analysis of the fully-discrete scheme is presented by employing some important lemmas. At the same time, both the spatial superclose property in H-1-norm and convergence result in L-2-norm are derived by skillfully dealing with numerical errors without any restrictions of time step tau and mesh size h. As a necessary way for obtaining the aimed numerical analysis, the relationship between the nonstandard projection operator R-h and the interpolation operator I-h of linear triangle finite element is introduced. Moreover, the global superconvergence is deduced by adopting interpolation postprocessing technique. Finally, numerical tests are provided to illustrate the efficiency and correctness of the theoretical results. (C) 2018 Elsevier Ltd. All rights reserved.
关键词	Multi-term time-fractional mixed diffusion-wave equations Linear triangle finite element L1 time-stepping method Crank-Nicolson scheme Unconditional stability Convergence and superconvergence
DOI	10.1016/j.camwa.2018.11.028
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:000482248100035
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/35380
专题	计算数学与科学工程计算研究所
通讯作者	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.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
推荐引用方式 GB/T 7714	Zhao, Yanmin,Wang, Fenling,Hu, Xiaohan,et al. Anisotropic linear triangle finite element approximation for multi-term time-fractional mixed diffusion and diffusion-wave equations with variable coefficient on 2D bounded domain[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2019,78(5):1705-1719.
APA	Zhao, Yanmin,Wang, Fenling,Hu, Xiaohan,Shi, Zhengguang,&Tang, Yifa.(2019).Anisotropic linear triangle finite element approximation for multi-term time-fractional mixed diffusion and diffusion-wave equations with variable coefficient on 2D bounded domain.COMPUTERS & MATHEMATICS WITH APPLICATIONS,78(5),1705-1719.
MLA	Zhao, Yanmin,et al."Anisotropic linear triangle finite element approximation for multi-term time-fractional mixed diffusion and diffusion-wave equations with variable coefficient on 2D bounded domain".COMPUTERS & MATHEMATICS WITH APPLICATIONS 78.5(2019):1705-1719.