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《Pure and Applied Mathematics》 2009-04
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Superconvergence analysis and extrapolation of a new mixed finite element model for second order elliptic problem

SHI Dong-yang 1,WANG Hui-min 1,2 (1.Deparment of Mathematics,Zhengzhou University,Zhengzhou 450052,China;2.Department of Mathematics and Physics,Henan Institute of Engineering,Zhengzhou 450007,China)  
A new mixed finite element model for the second order elliptic problem is presented by supplementing way.The superclose properties of the exact solution and the approximate solution of ECHL element are derived through integral identity technique on anisotropic meshes.At the same time,based on the interpolated postprocessing technique,the global superconvergence is obtained.Furthermore,one order higher convergence rate than the general error estimate is derived using asymptotic error expansion and the extrapolation.
【Fund】: 国家自然科学基金(10671184)
【CateGory Index】: O242.21
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【Citations】
Chinese Journal Full-text Database 2 Hits
1 Duan Huoyuan Liang Guoping (Academy of Mathematics and System Sciences, Institute of Mathematics Chinese Academy of Sciences, Beijing, 100080);MIXED FINITE ELEMENT METHODS FOR THE 2ND-ORDER ELLIPTIC PROBLEM[J];Mathematica Numerica Sinica;2001-04
2 Shi Dongyang (Department of Mathematics, Zhengzhou University, Zhengzhou 450002, China) Liang Hui (Department of Mathematics, Zhengzhou University, Zhengzhou 450002, China; School of Science, Harbin Institute of Technology, Harbin 150001, China);SUPERCONVERGENCE ANALYSIS AND EXTRAPOLATION OF A NEW UNCONVENTIONAL HERMITE-TYPE ANISOTROPIC RECTANGULAR ELEMENT[J];Mathematica Numerica Sinica;2005-04
【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 LIN Jia-fu, LEI Jun-li(School of Science, Beijing Institute of Technology, Beijing100081, China);The Multi-Parameter Extrapolation of the Hood-Taylor Elements for the Stokes Problem[J];Journal of Beijing Institute of Technology;2004-11
2 LI Cui-zhe, LI Zhi-yan(School of Science, Beijing Institute of Technology, Beijing100081, China);Existence of Solutions of Third-Order p-Laplacian Resonant Multi-Point Boundary Value Problems[J];Journal of Beijing Institute of Technology;2004-11
3 LIN Jia-fu,LI Qian(School of Science,Beijing Institute of Technology,Beijing100081,China);Superconvergence of the Bernadi-Raugel Mixed Finite Element Approximation for the Three-Dimensional Stokes Problem[J];Journal of Beijing Institute of Technology;2005-12
4 YUAN Jing(School of Mathematics and Physics,North China Electric Power University,Beijing 102206,China);Extrapolation of the Eigenvalue on Bilinear Element[J];Journal of Beijing Union University(Natural Sciences);2006-04
5 LI Ling-ling~1,SHI Dong-yang~2 (1.Pingdingshan Institute of Technology,Pingdingshan 467000,China;2.Zhengzhou University,Zhengzhou 450052,China);Convergence analysis for second order parabolic equation with anisotropic constringency[J];Journal of Pingdingshan Institute of Technology;2006-03
6 SONG Yong-zhi1,FAN Chuan-qiang2(1.School of Mathematics and Science,Xuchang University,Xuchang Henan 461000,P.R.China;2.School of Science,Liaoning University of Petroleum & Chemical Technology,Fushun Liaoning 113001,P.R.China);Research on the Bulk Superconvergence of the R-T Elements Solution to Parabolic Equation[J];Journal of Liaoning University of Petroleum & Chemical Technology;2008-02
7 YANG Yi-du (Central of Network, Guizhou Normal University, Guiyang 550001);A Finite Element Defect Correction Scheme and Lower Bounds for the Eigenvalue[J];Chinese Journal of Engineering Mathematics;2006-01
8 SHI Dong-yang1, PENG Yu-cheng1,2 (1- Department of Mathematics, Zhengzhou University, Zhengzhou 450052; 2- Department of Mathematics, Xinyang Normal University, Henan, Xinyang 464000);The Finite Element Methods for Fourth Order Eigenvalue Problems on Anisotropic Meshes[J];Chinese Journal of Engineering Mathematics;2008-06
9 SHI Dong-yang, WANG Hai-hong (Deparment of Mathematics, Zhengzhou University, Zhengzhou 450052);Anisotropic Nonconforming Finite Element Analysis for Integro-differential Equations of Parabolic Type[J];Chinese Journal of Engineering Mathematics;2009-02
10 Chen Zhen Yang Yidu (School of Mathematics and Computer Sciences, Guizhou Normal University, Guiyang 550001);THE GLOBAL STRESS SUPERCONVERGENCE OF WILSON'S BRICK[J];Numerical Mathematics A Journal of Chinese Universities;2005-S1
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