A V-cycle mutigrid for quadrilateral rotated Q(1) element with numerical integration

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	A V-cycle mutigrid for quadrilateral rotated Q(1) element with numerical integration
	Shi, ZC; Xu, XJ
	2003-09-01
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	21 期号:5 页码:545-554
摘要	The rotated Q(1) nonconforming element first proposed and used to solve the Stokes problem by Rannacher and Turek in [12]. Kloucek, Li and Luskin have implemented it to simulate the martensitic crystals with microstructures [9], [10]. Recently, Shi and Ming [14] gave a detailed mathematics analysis for this element under the bi-section condition for mesh subdivisions, which was first introduced by Shi [13] for analyzing the quadrilateral Wilson element. Meanwhile they also proposed some effective numerical quadrature schemes for this element[14]. Moreover, they have succeeded in using this element for the Mindlin-Reissner plate problem [11]. Quasi-optimal maximum norm estimations for the quadrilateral rotated Q(1) element approximation of Navier-Stokes equations were established in [17]. In this paper, we will investigate multigrid methods for solving discrete algebraic equations obtained by use of the quadrilateral rotated Q(1) elements. An effective V-cycle multigrid algorithm is presented with numerical integrations. A uniform convergence factor is obtained. A similar idea has been exploited for the Wilson nonconforming element [15] and the TRUNC plate element [16]. We also mention that some nonconforming multigrid algorithms for the second order problem are studied in early papers, see [1], [6] for P-1 nonconforming element, and [8] for the rectangular rotated Q(1) element. The outline of the paper is as follows. In section 2, we introduce the quadrilateral rotated Q(1) element. In the last section an effective V-cycle multigrid algorithm is presented.
关键词	multigrid rotated Q(1) elements numerical integration
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000185366900001
出版者	VSP BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/18951
专题	中国科学院数学与系统科学研究院
通讯作者	Shi, ZC
作者单位	Chinese Acad Sci, LSEC, Inst Computat Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Shi, ZC,Xu, XJ. A V-cycle mutigrid for quadrilateral rotated Q(1) element with numerical integration[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2003,21(5):545-554.
APA	Shi, ZC,&Xu, XJ.(2003).A V-cycle mutigrid for quadrilateral rotated Q(1) element with numerical integration.JOURNAL OF COMPUTATIONAL MATHEMATICS,21(5),545-554.
MLA	Shi, ZC,et al."A V-cycle mutigrid for quadrilateral rotated Q(1) element with numerical integration".JOURNAL OF COMPUTATIONAL MATHEMATICS 21.5(2003):545-554.