Adaptive finite element method for parabolic equations with Dirac measure

doi:10.1016/j.cma.2017.08.051

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	Adaptive finite element method for parabolic equations with Dirac measure
	Gong, Wei1 ; Liu, Huipo 2; Yan, Ningning3
	2018
发表期刊	COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
ISSN	0045-7825
卷号	328 页码:217-241
摘要	In this paper we study the adaptive finite element method for parabolic equations with Dirac measure. Two kinds of problems with separate measure data in time and measure data in space are considered. It is well known that the solutions of such kind of problems may exhibit lower regularity due to the existence of the Dirac measure, and thus fit to adaptive FEM for space discretization and variable time steps for time discretization. For both cases we use piecewise linear and continuous finite elements for the space discretization and backward Euler scheme, or equivalently piecewise constant discontinuous Galerkin method, for the time discretization, the a posteriori error estimates based on energy and L-2 norms for the fully discrete problems are then derived to guide the adaptive procedure. Numerical results are provided at the end of the paper to support our theoretical findings. (C) 2017 Elsevier B.V. All rights reserved.
关键词	Parabolic equation Dirac measure Adaptive finite element method Space-time discretization A posteriori error estimates
DOI	10.1016/j.cma.2017.08.051
语种	英语
资助项目	National Natural Science Foundation of China[11001027] ; National Natural Science Foundation of China[11571356] ; National Natural Science Foundation of China[11671391] ; National Natural Science Foundation of China[11771053] ; National Natural Science Foundation of China[91530204] ; National Basic Research Program[2011CB309705] ; National Basic Research Program[2012CB821204]
WOS研究方向	Engineering ; Mathematics ; Mechanics
WOS类目	Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics
WOS记录号	WOS:000416218500010
出版者	ELSEVIER SCIENCE SA
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/124
专题	国家数学与交叉科学中心系统科学研究所计算数学与科学工程计算研究所
通讯作者	Gong, Wei
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, NCMIS,LSEC, Beijing 100190, Peoples R China 2.Inst Appl Phys & Computat Math, Beijing 100094, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, NCMIS,LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Gong, Wei,Liu, Huipo,Yan, Ningning. Adaptive finite element method for parabolic equations with Dirac measure[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,2018,328:217-241.
APA	Gong, Wei,Liu, Huipo,&Yan, Ningning.(2018).Adaptive finite element method for parabolic equations with Dirac measure.COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,328,217-241.
MLA	Gong, Wei,et al."Adaptive finite element method for parabolic equations with Dirac measure".COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 328(2018):217-241.