Iterative two-grid methods for semilinear elliptic equations

doi:10.1016/j.camwa.2020.04.004

CSpace

	Iterative two-grid methods for semilinear elliptic equations
	Zhang, Weifeng 1,2; Fan, Ronghong 3,4; Zhong, Liuqiang 5
	2020-08-01
发表期刊	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
卷号	80 期号:3 页码:522-530
摘要	We design and analyze a new finite element discretization technique based on iterative two-grid methods for semilinear elliptic partial differential equations (PDEs). We first present an iterative two-grid method that just applies the classical two-grid for semilinear elliptic PDEs in a successive fashion, namely, to solve a semilinear problem on the coarse space and then to solve a symmetric positive definite problem on the fine space. Thus, we only need to deal with semilinear problems in the coarse space in the first algorithm. Secondly, we replace the semilinear term by using the corresponding first order Taylor expansion in the second iterative two-grid. We provide the error estimates for the second iterative algorithm and present numerical experiments to show the efficiency of our methods. (C) 2020 Elsevier Ltd. All rights reserved.
关键词	Iterative methods Two-grid method Convergence Semilinear elliptic equations
DOI	10.1016/j.camwa.2020.04.004
收录类别	SCI
语种	英语
资助项目	Science Challenge Project, China[TZ2016003] ; National Natural Science Foundation of China[11971472] ; National Natural Science Foundation of China[11671159] ; Natural Science Foundation of Guangdong Province, China[2016A030313842] ; Natural Science Foundation of Guangdong Province, China[2019A1515010724] ; Characteristic Innovation Projects of Guangdong Colleges and Universities, China[2018KTSCX044] ; General Project topic of Science and Technology in Guangzhou, China[201904010117]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000536117200007
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51517
专题	中国科学院数学与系统科学研究院
通讯作者	Zhong, Liuqiang
作者单位	1.Kunming Univ Sci & Technol, Dept Engn Mech, Kunming 650500, Yunnan, Peoples R China 2.Kunming Univ Sci & Technol, Dept Appl Math, Kunming 650500, Yunnan, Peoples R China 3.Acad Math & Syst Sci, NCMIS, Beijing 100190, Peoples R China 4.Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China 5.South China Normal Univ, Sch Math Sci, Guangzhou 510631, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Weifeng,Fan, Ronghong,Zhong, Liuqiang. Iterative two-grid methods for semilinear elliptic equations[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2020,80(3):522-530.
APA	Zhang, Weifeng,Fan, Ronghong,&Zhong, Liuqiang.(2020).Iterative two-grid methods for semilinear elliptic equations.COMPUTERS & MATHEMATICS WITH APPLICATIONS,80(3),522-530.
MLA	Zhang, Weifeng,et al."Iterative two-grid methods for semilinear elliptic equations".COMPUTERS & MATHEMATICS WITH APPLICATIONS 80.3(2020):522-530.