AN ADAPTIVE IMMERSED FINITE ELEMENT METHOD WITH ARBITRARY LAGRANGIAN-EULERIAN SCHEME FOR PARABOLIC EQUATIONS IN TIME VARIABLE DOMAINS

	AN ADAPTIVE IMMERSED FINITE ELEMENT METHOD WITH ARBITRARY LAGRANGIAN-EULERIAN SCHEME FOR PARABOLIC EQUATIONS IN TIME VARIABLE DOMAINS
	Chen, Zhiming1 ; Wu, Zedong 2; Xiao, Yuanming 3
	2015
发表期刊	INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
ISSN	1705-5105
卷号	12 期号:3 页码:567-591
摘要	We first propose an adaptive immersed finite element method based on the a posteriori error estimate for solving elliptic equations with non-homogeneous boundary conditions in general Lipschitz domains. The underlying finite element mesh need not fit the boundary of the domain. Optimal a priori error estimate of the proposed immersed finite element method is proved. The immersed finite element method is then used to solve parabolic problems in time variable domains together with an arbitrary Lagrangian-Eulerian (ALE) time discretization scheme. An a posteriori error estimate for the fully discrete immersed finite element method is derived which can be used to adaptively update the time step sizes and finite element meshes at each time step. Numerical experiments are reported to support the theoretical results.
关键词	Immersed finite element adaptive a posteriori error estimate time variable domain
语种	英语
资助项目	National Basic Research Project[2011CB309700] ; China NSF[11021101] ; China NSF[11321061] ; China NSF[11101208] ; Fundamental Research Funds for the Central Universities[1118020303]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000361156800007
出版者	ISCI-INST SCIENTIFIC COMPUTING & INFORMATION
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/20753
专题	计算数学与科学工程计算研究所
通讯作者	Chen, Zhiming
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, Beijing 100190, Peoples R China 3.Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China
推荐引用方式 GB/T 7714	Chen, Zhiming,Wu, Zedong,Xiao, Yuanming. AN ADAPTIVE IMMERSED FINITE ELEMENT METHOD WITH ARBITRARY LAGRANGIAN-EULERIAN SCHEME FOR PARABOLIC EQUATIONS IN TIME VARIABLE DOMAINS[J]. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING,2015,12(3):567-591.
APA	Chen, Zhiming,Wu, Zedong,&Xiao, Yuanming.(2015).AN ADAPTIVE IMMERSED FINITE ELEMENT METHOD WITH ARBITRARY LAGRANGIAN-EULERIAN SCHEME FOR PARABOLIC EQUATIONS IN TIME VARIABLE DOMAINS.INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING,12(3),567-591.
MLA	Chen, Zhiming,et al."AN ADAPTIVE IMMERSED FINITE ELEMENT METHOD WITH ARBITRARY LAGRANGIAN-EULERIAN SCHEME FOR PARABOLIC EQUATIONS IN TIME VARIABLE DOMAINS".INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING 12.3(2015):567-591.