Two Mixed Finite Element Methods for Time-Fractional Diffusion Equations

doi:10.1007/s10915-015-0152-y

	Two Mixed Finite Element Methods for Time-Fractional Diffusion Equations
	Zhao, Yanmin 1; Chen, Pan 2; Bu, Weiping 3; Liu, Xiangtao 4; Tang, Yifa5
	2017
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	70 期号:1 页码:407-428
摘要	Based on spatial conforming and nonconforming mixed finite element methods combined with classical L1 time stepping method, two fully-discrete approximate schemes with unconditional stability are first established for the time-fractional diffusion equation with Caputo derivative of order . As to the conforming scheme, the spatial global superconvergence and temporal convergence order of for both the original variable u in -norm and the flux in -norm are derived by virtue of properties of bilinear element and interpolation postprocessing operator, where h and are the step sizes in space and time, respectively. At the same time, the optimal convergence rates in time and space for the nonconforming scheme are also investigated by some special characters of nonconforming element, which manifests that convergence orders of and for the original variable u in broken -norm and -norm, respectively, and approximation for the flux converging with order in -norm. Numerical examples are provided to demonstrate the theoretical analysis.
关键词	Mixed finite element methods L1 method Time-fractional diffusion equation Unconditional stability Superconvergence and convergence
DOI	10.1007/s10915-015-0152-y
语种	英语
资助项目	National Natural Science Foundation of China[11101381] ; National Natural Science Foundation of China[11371357] ; Outstanding Young Talents Training Plan by Xuchang University
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000391930500017
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/24564
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.Huainan Vocat & Tech Coll, Div Basic Educ, Huainan 232001, Peoples R China 3.Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Peoples R China 4.Cipher Ground, 675 Rt 1 South, North Brunswick, NJ 08902 USA 5.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zhao, Yanmin,Chen, Pan,Bu, Weiping,et al. Two Mixed Finite Element Methods for Time-Fractional Diffusion Equations[J]. JOURNAL OF SCIENTIFIC COMPUTING,2017,70(1):407-428.
APA	Zhao, Yanmin,Chen, Pan,Bu, Weiping,Liu, Xiangtao,&Tang, Yifa.(2017).Two Mixed Finite Element Methods for Time-Fractional Diffusion Equations.JOURNAL OF SCIENTIFIC COMPUTING,70(1),407-428.
MLA	Zhao, Yanmin,et al."Two Mixed Finite Element Methods for Time-Fractional Diffusion Equations".JOURNAL OF SCIENTIFIC COMPUTING 70.1(2017):407-428.