ON THE INTERPOLATION ERROR ESTIMATES FOR Q(1) QUADRILATERAL FINITE ELEMENTS

doi:10.1137/070700486

	ON THE INTERPOLATION ERROR ESTIMATES FOR Q(1) QUADRILATERAL FINITE ELEMENTS
	Mao, Shipeng1 ; Nicaise, Serge 2; Shi, Zhong-Ci1
	2008
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	47 期号:1 页码:467-486
摘要	In this paper, we study the relation between the error estimate of the bilinear interpolation on a general quadrilateral and the geometric characters of the quadrilateral. Some explicit bounds of the interpolation error are obtained based on some sharp estimates of the integral over 1/\|J\|(p-1) for 1 <= p <= infinity on the reference element, where J is the Jacobian of the nona. ne mapping. This allows us to introduce weak geometric conditions (depending on p) leading to interpolation error estimates in the W-1, (p) norm, for any p is an element of [1, infinity), which can be regarded as a generalization of the regular decomposition property (RDP) condition introduced in [ G. Acosta and R. G. Duran, SIAM J. Numer. Anal., 38 ( 2000), pp. 1073-1088] for p = 2 and new RDP conditions (NRDP) for p not equal 2. We avoid the use of the reference family elements, which allows us to extend the results to a larger class of elements and to introduce the NRDP condition in a more unified way. As far as we know, the mesh condition presented in this paper is weaker than any other mesh conditions proposed in the literature for any p with 1 <= p <= infinity.
关键词	error estimates quadrilateral elements isoparametric finite elements maximal angle condition
DOI	10.1137/070700486
语种	英语
资助项目	National Basic Research Program of China[2005CB321701]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000263103800022
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/5895
专题	计算数学与科学工程计算研究所
通讯作者	Mao, Shipeng
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China 2.Univ Valenciennes & Hainaut Cambresis, LAMAV, ISTV, F-59313 Valenciennes 9, France
推荐引用方式 GB/T 7714	Mao, Shipeng,Nicaise, Serge,Shi, Zhong-Ci. ON THE INTERPOLATION ERROR ESTIMATES FOR Q(1) QUADRILATERAL FINITE ELEMENTS[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2008,47(1):467-486.
APA	Mao, Shipeng,Nicaise, Serge,&Shi, Zhong-Ci.(2008).ON THE INTERPOLATION ERROR ESTIMATES FOR Q(1) QUADRILATERAL FINITE ELEMENTS.SIAM JOURNAL ON NUMERICAL ANALYSIS,47(1),467-486.
MLA	Mao, Shipeng,et al."ON THE INTERPOLATION ERROR ESTIMATES FOR Q(1) QUADRILATERAL FINITE ELEMENTS".SIAM JOURNAL ON NUMERICAL ANALYSIS 47.1(2008):467-486.