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二阶椭圆问题的各向异性非协调Crouzeix-Raviart型有限元方法

石东洋 许超

石东洋, 许超. 二阶椭圆问题的各向异性非协调Crouzeix-Raviart型有限元方法[J]. 应用数学和力学, 2012, 33(2): 240-249. doi: 10.3879/j.issn.1000-0887.2012.02.009
引用本文: 石东洋, 许超. 二阶椭圆问题的各向异性非协调Crouzeix-Raviart型有限元方法[J]. 应用数学和力学, 2012, 33(2): 240-249. doi: 10.3879/j.issn.1000-0887.2012.02.009
SHI Dong-yang, XU Chao. Anisotropic Nonconforming Crouzeix-Raviart Type FEM for Second Order Elliptic Problems[J]. Applied Mathematics and Mechanics, 2012, 33(2): 240-249. doi: 10.3879/j.issn.1000-0887.2012.02.009
Citation: SHI Dong-yang, XU Chao. Anisotropic Nonconforming Crouzeix-Raviart Type FEM for Second Order Elliptic Problems[J]. Applied Mathematics and Mechanics, 2012, 33(2): 240-249. doi: 10.3879/j.issn.1000-0887.2012.02.009

二阶椭圆问题的各向异性非协调Crouzeix-Raviart型有限元方法

doi: 10.3879/j.issn.1000-0887.2012.02.009
基金项目: 国家自然科学基金资助项目(10971203)
详细信息
    通讯作者:

    石东洋(1961—),男, 河南鲁山人,教授,博士 (联系人. Tel: +86-371-67767813;E-mail:shi-dy@zzu.edu.cn);许超(1975—),男,河南洛阳人,副教授,硕士(Tel: +86-379-65928279;E-mail:xc-lyct@126.com).

  • 中图分类号: O242.21

Anisotropic Nonconforming Crouzeix-Raviart Type FEM for Second Order Elliptic Problems

  • 摘要: 对满足最大角条件和坐标系条件的二维区域中的各向异性一般三角形网格,研究了二阶椭圆问题的非协调Crouzeix-Raviart型线性三角形有限元逼近,得到了最优的能量模和L2-模误差估计结果.
  • [1] Ciarlet P G. The Finite Element Method for Elliptic Problems[M]. Amsterdam: North-Holland, 1978.
    [2] Apel T, Dobrowolski M. Anisotropic interpolation with applications to the finite element method[J]. Computing, 1992, 47(2/3): 277-293.
    [3] Apel T. Anisotropic Finite Elements: Local Estimates and Applications[M]. Stuttgart, Leipzig: B G Teubner, 1999.
    [4] Chen S C, Shi D Y, Zhao Y C. Anisotropic interpolations and quasi-Wilson element for narrow quadrilateral meshes[J]. IMA Journal of Numerical Analysis, 2004, 24(1): 77-95.
    [5] Chen S C, Zhao Y C, Shi D Y. Anisotropic interpolations with application to nonconforming elements[J]. Applied Numerical Mathematics, 2004, 49: 135-152.
    [6] 石东洋, 梁慧. 各向异性网格下Wilson元的超收敛分析[J]. 应用数学和力学, 2007, 28(1): 107-113.(SHI Dong-yang, LIANG Hui. Superconvergence analysis of Wilson element on anisotropic meshes[J].Applied Mathematics and Mechanics(English Edition), 2007, 28(1): 119-125.)
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    [8] Shi D Y, Chen S C, Hagiwara I. Convergence analysis for a nonconforming membrane element on anisotropic meshes[J]. Journal of Computational Mathematics, 2005, 23(4): 373-382.
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    [11] Lin Q, Lutz T, Zhou A H. Superconvergence and extrapolation of non-conforming low order finite elements applied to the Poisson equation[J]. IMA Journal of Numerical Analysis, 2005, 25(1): 160-181.
    [12] Shi D Y, Mao S P, Chen S C. Anisotropic nonconforming finite element with some superconvergence results[J]. Journal of Computational Mathematics, 2005, 23(3): 261-274.
    [13] Shi D Y, Pei L F. Low order Crouzeix-Raviart type nonconforming finite element methods for approximating Maxwell’s equations[J]. International Journal of Numerical Analysis and Modeling, 2008, 5(3): 373-385.
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    [17] Shi D Y, Guan H B. A class of Crouzeix-Raviart type nonconforming finite element methods for parabolic variational inequality problem with moving grid on anisotropic meshes[J].Hokkaido Mathematical Journal, 2007, 36(4): 687-709.
    [18] Shi D Y, Ren J C, Hao X B. A new second order nonconforming mixed finite element scheme for the stationary Stokes and Navier-Stokes equations[J]. Applied Mathematics and Computation, 2009, 207(2): 462-477.
    [19] Shi D Y, Liang H. Convergence and superconvergence analysis of a new quadratic Hermite-type triangular element on anisotropic meshes[J]. Applied Mathematics and Computation, 2009, 212(1): 257-269.
    [20] Shi D Y, Xie P L. Morley type non-C0 nonconforming rectangular plate finite elements on anisotropic meshes[J]. Numerical Methods for Partial Differential Equations, 2010, 26(3): 723-744.
    [21] Shi D Y, Wang X L. Two low order characteristic finite element methods for a convection-dominated transport problem[J]. Computers and Mathematics With Applications, 2010, 59(12): 3630-3639.
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  • 被引次数: 0
出版历程
  • 收稿日期:  2011-09-15
  • 修回日期:  2011-11-07
  • 刊出日期:  2012-02-15

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