THE BEST L-2 NORM ERROR ESTIMATE OF LOWER ORDER FINITE ELEMENT METHODS FOR THE FOURTH ORDER PROBLEM

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	THE BEST L-2 NORM ERROR ESTIMATE OF LOWER ORDER FINITE ELEMENT METHODS FOR THE FOURTH ORDER PROBLEM
其他题名	THE BEST L2 NORM ERROR ESTIMATE OF LOWER ORDERFINITE ELEMENT METHODS FOR THE FOURTH ORDERPROBLEM
	Hu Jun 1; Shi ZhongCi 2
	2012
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	30 期号:5 页码:449-460
摘要	In the paper, we analyze the L-2 norm error estimate of lower order finite element methods for the fourth order problem. We prove that the best error estimate in the L-2 norm of the finite element solution is of second order, which can not be improved generally. The main ingredients are the saturation condition established for these elements and an identity for the error in the energy norm of the finite element solution. The result holds for most of the popular lower order finite element methods in the literature including: the Powell-Sabin C-1-P-2 macro element, the nonconforming Morley element, the C-1-Q(2) macro element, the nonconforming rectangle Morley element, and the nonconforming incomplete biquadratic element. In addition, the result actually applies to the nonconforming Adini element, the nonconforming Fraeijs de Veubeke elements, and the nonconforming Wang-Xu element and the Wang-Shi-Xu element provided that the saturation condition holds for them. This result solves one long standing problem in the literature: can the L-2 norm error estimate of lower order finite element methods of the fourth order problem be two order higher than the error estimate in the energy norm?
其他摘要	In the paper, we analyze the L2 norm error estimate of lower order finite elementmethods for the fourth order problem. We prove that the best error estimate in the L2norm of the finite element solution is of second order, which can not be improved generally.The main ingredients are the saturation condition established for these elements and anidentity for the error in the energy norm of the finite element solution. The result holdsfor most of the popular lower order finite element methods in the literature including: thePowell-Sabin C~1-P~2 macro element, the nonconforming Morley element, the C1-Q2 macroelement, the nonconforming rectangle Morley element, and the nonconforming incompletebiquadratic element. In addition, the result actually applies to the nonconforming Adinielement, the nonconforming Fraeijs de Veubeke elements, and the nonconforming Wang-Xu element and the Wang-Shi-Xu element provided that the saturation condition holdsfor them. This result solves one long standing problem in the literature: can the L2 normerror estimate of lower order finite element methods of the fourth order problem be twoorder higher than the error estimate in the energy norm?
关键词	ELLIPTIC-EQUATIONS BOUNDS L-2 norm error estimate Energy norm error estimate Conforming Nonconforming The Kirchhoff plate
收录类别	CSCD
语种	英语
资助项目	[NSFC] ; [NSFC projection] ; [Chinesisch-Deutsches Zentrum project]
CSCD记录号	CSCD:4665765
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52835
专题	中国科学院数学与系统科学研究院
作者单位	1.北京大学 2.中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Hu Jun,Shi ZhongCi. THE BEST L-2 NORM ERROR ESTIMATE OF LOWER ORDER FINITE ELEMENT METHODS FOR THE FOURTH ORDER PROBLEM[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2012,30(5):449-460.
APA	Hu Jun,&Shi ZhongCi.(2012).THE BEST L-2 NORM ERROR ESTIMATE OF LOWER ORDER FINITE ELEMENT METHODS FOR THE FOURTH ORDER PROBLEM.JOURNAL OF COMPUTATIONAL MATHEMATICS,30(5),449-460.
MLA	Hu Jun,et al."THE BEST L-2 NORM ERROR ESTIMATE OF LOWER ORDER FINITE ELEMENT METHODS FOR THE FOURTH ORDER PROBLEM".JOURNAL OF COMPUTATIONAL MATHEMATICS 30.5(2012):449-460.