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 THE BEST L2 NORM ERROR ESTIMATE OF LOWER ORDERFINITE ELEMENT METHODS FOR THE FOURTH ORDERPROBLEM Hu Jun1; Shi Zhongci2 2012 Source Publication Journal of Computational Mathematics ISSN 0254-9409 Volume 30Issue:5Pages:449 Abstract 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? Language 英语 Funding Project [NSFC] ; [NSFC projection] ; [Chinesisch-Deutsches Zentrum project] Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/49957 Collection 计算数学与科学工程计算研究所 Affiliation 1.北京大学2.中国科学院数学与系统科学研究院 Recommended CitationGB/T 7714 Hu Jun,Shi Zhongci. THE BEST L2 NORM ERROR ESTIMATE OF LOWER ORDERFINITE ELEMENT METHODS FOR THE FOURTH ORDERPROBLEM[J]. Journal of Computational Mathematics,2012,30(5):449. APA Hu Jun,&Shi Zhongci.(2012).THE BEST L2 NORM ERROR ESTIMATE OF LOWER ORDERFINITE ELEMENT METHODS FOR THE FOURTH ORDERPROBLEM.Journal of Computational Mathematics,30(5),449. MLA Hu Jun,et al."THE BEST L2 NORM ERROR ESTIMATE OF LOWER ORDERFINITE ELEMENT METHODS FOR THE FOURTH ORDERPROBLEM".Journal of Computational Mathematics 30.5(2012):449.
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