A FULL MULTIGRID METHOD FOR SEMILINEAR ELLIPTIC EQUATION

doi:10.21136/AM.2017.0344-16

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	A FULL MULTIGRID METHOD FOR SEMILINEAR ELLIPTIC EQUATION
	Xu, Fei 1; Xie, Hehu2,3
刊名	APPLICATIONS OF MATHEMATICS
	2017-06-01
卷号	62 期号:3 页码:225-241
关键词	semilinear elliptic problem full multigrid method multilevel correction finite element method
ISSN号	0862-7940
DOI	10.21136/AM.2017.0344-16
英文摘要	A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and semilinear problems on a very low dimensional space. The linearized boundary value problems are solved by some multigrid iterations. Besides the multigrid iteration, all other efficient numerical methods can also serve as the linear solver for solving boundary value problems. The optimality of the computational work is also proved. Compared with the existing multigrid methods which need the bounded second order derivatives of the nonlinear term, the proposed method only needs the Lipschitz continuation in some sense of the nonlinear term.
资助项目	National Natural Science Foundations of China (NSFC)[91330202] ; National Natural Science Foundations of China (NSFC)[11371026] ; National Natural Science Foundations of China (NSFC)[11001259] ; National Natural Science Foundations of China (NSFC)[11031006] ; National Natural Science Foundations of China (NSFC)[2011CB309703] ; National Center for Mathematics and Interdisciplinary Science, CAS
WOS研究方向	Mathematics
语种	英语
出版者	ACAD SCIENCES CZECH REPUBLIC, INST MATHEMATICS
WOS记录号	WOS:000403537700002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/25565]
专题	计算数学与科学工程计算研究所
通讯作者	Xu, Fei
作者单位	1.Beijing Univ Technol, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, 55 Zhongguancun Donglu, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Xu, Fei,Xie, Hehu. A FULL MULTIGRID METHOD FOR SEMILINEAR ELLIPTIC EQUATION[J]. APPLICATIONS OF MATHEMATICS,2017,62(3):225-241.
APA	Xu, Fei,&Xie, Hehu.(2017).A FULL MULTIGRID METHOD FOR SEMILINEAR ELLIPTIC EQUATION.APPLICATIONS OF MATHEMATICS,62(3),225-241.
MLA	Xu, Fei,et al."A FULL MULTIGRID METHOD FOR SEMILINEAR ELLIPTIC EQUATION".APPLICATIONS OF MATHEMATICS 62.3(2017):225-241.