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《Chinese Journal of Engineering Mathematics》 2006-01
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A Finite Element Defect Correction Scheme and Lower Bounds for the Eigenvalue

YANG Yi-du (Central of Network, Guizhou Normal University, Guiyang 550001)  
This paper considers a kind of finite element defect correction scheme which possesses low computing complexities for the linear finite element method solving the second-order elliptic eigenvalue problem. Based on the interpolated correction and the Rayleigh quotient, a new corrected eigenvalue is obtained. Theoretical analysis shows the corrected eigenvalue either achieves the convergence order of the quadratic finite element eigenvalue, or approximates the accurate eigenvalue from the below as the mesh size sufficiently small. Numerical experiments are provided to support our theoretical conclusions.
【Fund】: 贵州省科学技术基金
【CateGory Index】: O241.82
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【References】
Chinese Journal Full-text Database 3 Hits
1 HU Jun-mei,SHI Yi-min,GAO Ni,QIN Xiao-qiong (Department of Applied Mathematics,Northwestern Polytechnical University,Xi’an 710072);Empirical Bayes Estimation and Application for the Environmental Factor of Two-parameter Rayleigh Distribution[J];Chinese Journal of Engineering Mathematics;2010-01
2 YANG YiDu & FAN XinYue School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, China;Generalized Rayleigh quotient and finite element two-grid discretization schemes[J];中国科学(A辑:数学)(英文版);2009-09
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Chinese Journal Full-text Database 2 Hits
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【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 ZHOU Jia-quan1,SHI Dong-wei2,ZHANG Yong-sheng1(1.Department of Mathematics and Physics,Luoyang Institute of Technology,Luoyang 471023,China; 2.Department of Mathematics,Henan Institute of Science and Technology,Xinxiang 453003,China);An H~1-Galerkin nonconforming mixed finite element method of Schrdinger equation[J];Journal of Anhui University(Natural Science Edition);2012-01
2 Leng Xiang (Dept.of Economics,Anhui Institute of Architecture,Hefei,230022) Abstract:In this paper we establish a unifying mathematical basis for the;A UNIFYING ANALYSIS OF NONCONFORMING AND UNCONVENTIONAL ELEMENTS FOR KIR CHHOFF PLATE BENDING PROBLEMS Ⅱ MATHEMATICAL THEORYOF ABSTRACT ERROR ANALYSIS[J];JOURNAL OF ANHUI INSTITUTE OF ARCHITECTURE;2000-01
3 Zhang Weilin (Computing Center,Anhui Institute of Architecture,Hefei,230022);STUDYING STATUS AND DEVELOPMENT OF COMPUTING MECHANICS[J];JOURNAL OF ANHUI INSTITUTE OF ARCHITECTURE;2001-02
4 Leng Xiang (Dept.of Economics,Anhui Institute of Architecture,Hefei,230022);A UNIF YING ANALYSIS OF NONCONFORMING AND UNCONVENTION AL ELEMENTS FOR KIR CHHOFF PLATE BENDING PROBLEMS ——I.CONSTRUCTION OF ELEMENTS[J];JOURNAL OF ANHUI INSTITUTE OF ARCHITECTURE;2001-02
5 ZOU Hui-jin(School of Mathematics,Hefei University of Technology,Hefei 230009,China);Convergence Analysis for Interracial and Differential Equation with Anisotropic Finite Element[J];Journal of Anqing Teachers College(Natural Science Edition);2010-03
6 Zhang Po (Department of Math ematics and Physics,North China Electric Power University,Baoding 071003 ,China);The Numerical Experiment of Expansion and Extrapolation of the Eigenvalue Problem on Wilson Element[J];Journal of Baoding University;2011-03
7 ZHU Shengzhi(School of Science,Beijing Jiaotong University,Beijing 100044,China);Superconvergence of Bernardi-Raugel mixed finite element approximation for Stokes problem on anisotropic meshes[J];Journal of Beijing Jiaotong University;2011-06
8 Feng Huihua Zuo Zhengxing Liao Ridong Zhang Yushen (School of Vehicle and Transportation Engineering, Beijing Institute of Technology, Beijing, 100081);FINITE ELEMENT ANALYSIS ON THE DYNAMIC CHARACTERISTICS OF HIGH EFFICIENCY DIESEL[J];Acta Armamentarii;2002-03
9 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
10 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
【Co-references】
Chinese Journal Full-text Database 7 Hits
1 Lin Jinguan Wang Haibin Liu Yingan Wei Bocheng (Department of Applied Mathematics,Southeast University, Nanjing 210096);Conditional Confidence Intervals of the Parameters for Two-Parameter Rayleigh Distribution Based on Type-Ⅱ Censored Samples[J];Journal of Southeast Univwrsity(Natural Science Edition);2001-02
2 ZHANG Chun-guo(Department of Mathematics,Hangzhou Dianzi University,Hangzhou 310018);Energy Decay Estimates of the Rayleigh Beam with a Pointwise Feedback[J];Chinese Journal of Engineering Mathematics;2007-06
3 YANG Yi-du (School of Mathematics and Computer Sciences, Guizhou Normal University, Guiyang 550001);Iterated Galerkin Method and Rayleigh Quotient for Accelerating Convergence of Eigenvalue Problems[J];Chinese Journal of Engineering Mathematics;2008-03
4 CAO Liqun GUI Junzhi ZHU Dechao& LUO JianlanInstitute of Computational Mathematics and Science-Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China;Center of Solid Research, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;Department of Applied Physics, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;Spectral analysis and numerical simulation for second order elliptic operator with highly oscillating coefficients in perforated domains with a periodic structure[J];中国科学A辑(英文版);2002-12
5 YANG YiDu & CHEN Zhen School of Mathematics and Computer Sciences,Guizhou Normal University,Guiyang 550001,China;The order-preserving convergence for spectral approximation of self-adjoint completely continuous operators[J];中国科学(A辑:数学)(英文版);2008-07
6 HU Bin (Institute of Electronic Engineering ,CAEP, Mianyang 621900, China);The Definition and Research Status of Environmental Factor[J];Information and Electronic Engineering;2003-01
7 Jinchao Xu, Aihui ZhouCenter for Computational Mathematics and Applications and Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802, USAInstitute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China;Local and Parallel Finite Element Algorithms for Eigenvalue Problems[J];应用数学学报(英文版);2002-02
【Secondary References】
Chinese Journal Full-text Database 3 Hits
1 HU Sha-sha,WEI Cheng-dong,QIU Yan(School of Mathematical Sciences,Guangxi TeachersEducation University,Nanning 530023,P.R.China);Environmental Factor Maximum Likelihood Estimation and Bayes Estimation in Gamma Distribution[J];Journal of Guangxi Teachers Education University(Natural Science Edition);2011-02
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