ANALYSIS FOR QUADRILATERAL MITC ELEMENTS FOR THE REISSNER-MINDLIN PLATE PROBLEM

	ANALYSIS FOR QUADRILATERAL MITC ELEMENTS FOR THE REISSNER-MINDLIN PLATE PROBLEM
	Hu, Jun 1,2; Shi, Zhong-Ci3
	2009
发表期刊	MATHEMATICS OF COMPUTATION
ISSN	0025-5718
卷号	78 期号:266 页码:673-711
摘要	The present paper is made up of two parts. In the first part, we study the mathematical stability and convergence of the quadrilateral MITC elements for the Reissner-Mindlin plate problem in an abstract setting. We generalize the Brezzi-Bathe-Fortin conditions to the quadrilateral MITC elements by weakening the second and fourth conditions. Under these conditions, we show the well-posedness of the discrete problem and establish an abstract error estimate in the energy norm. The conclusion of this part is sparsity in the mathematical research of the quadrilateral MITC elements in the sense that one only needs to check these five conditions. In the second part, we extend four families of rectangular MITC elements of Stenberg and Suri to the quadrilateral meshes. We prove that these quadrilateral elements satisfy the generalized Brezzi-Bathe-Fortin conditions from the first part. We develop the h-p error estimates in both energy and L(2) norm for these quadrilateral elements. For the first three families of quadrilateral elements, the error estimates indicate that their convergent rates in both energy and L(2) norm depend on the mesh distortion parameter alpha. We can get optimal error estimates for them provided that alpha = 1. In addition, we show the optimal convergence rates in energy norm uniformly in alpha for the fourth family of quadrilateral elements. Like their rectangular counterparts, these quadrilateral elements are locking-free.
关键词	Reissner-Mandlin plate MITC quadrilateral element locking-free
语种	英语
资助项目	Special Funds for Major State Basic Research Project ; National Science Foundation of China[10601003] ; Author of National Excellent Doctoral Dissertation of PR China[200718]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000263026800003
出版者	AMER MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/9120
专题	计算数学与科学工程计算研究所
通讯作者	Hu, Jun
作者单位	1.Peking Univ, LMAM, Beijing 100871, Peoples R China 2.Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China 3.Chinese Acad Sci, Inst Computat Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Hu, Jun,Shi, Zhong-Ci. ANALYSIS FOR QUADRILATERAL MITC ELEMENTS FOR THE REISSNER-MINDLIN PLATE PROBLEM[J]. MATHEMATICS OF COMPUTATION,2009,78(266):673-711.
APA	Hu, Jun,&Shi, Zhong-Ci.(2009).ANALYSIS FOR QUADRILATERAL MITC ELEMENTS FOR THE REISSNER-MINDLIN PLATE PROBLEM.MATHEMATICS OF COMPUTATION,78(266),673-711.
MLA	Hu, Jun,et al."ANALYSIS FOR QUADRILATERAL MITC ELEMENTS FOR THE REISSNER-MINDLIN PLATE PROBLEM".MATHEMATICS OF COMPUTATION 78.266(2009):673-711.