A FULL MULTIGRID METHOD FOR SEMILINEAR ELLIPTIC EQUATION

doi:10.21136/AM.2017.0344-16

	A FULL MULTIGRID METHOD FOR SEMILINEAR ELLIPTIC EQUATION
	Xu, Fei 1; Xie, Hehu2,3
	2017-06-01
发表期刊	APPLICATIONS OF MATHEMATICS
ISSN	0862-7940
卷号	62 期号:3 页码:225-241
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.
关键词	semilinear elliptic problem full multigrid method multilevel correction finite element method
DOI	10.21136/AM.2017.0344-16
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000403537700002
出版者	ACAD SCIENCES CZECH REPUBLIC, INST MATHEMATICS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25566
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.