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平均间断有限元的强超收敛性及在Hamilton系统的应用

李灿华 陈传淼

李灿华, 陈传淼. 平均间断有限元的强超收敛性及在Hamilton系统的应用[J]. 应用数学和力学, 2011, 32(7): 883-894. doi: 10.3879/j.issn.1000-0887.2011.07.011
引用本文: 李灿华, 陈传淼. 平均间断有限元的强超收敛性及在Hamilton系统的应用[J]. 应用数学和力学, 2011, 32(7): 883-894. doi: 10.3879/j.issn.1000-0887.2011.07.011
LI Can-hua, CHEN Chuan-miao. Ultraconvergence for Averaging Discontinuous Finite Elements and Its Applications in Hamiltonian System[J]. Applied Mathematics and Mechanics, 2011, 32(7): 883-894. doi: 10.3879/j.issn.1000-0887.2011.07.011
Citation: LI Can-hua, CHEN Chuan-miao. Ultraconvergence for Averaging Discontinuous Finite Elements and Its Applications in Hamiltonian System[J]. Applied Mathematics and Mechanics, 2011, 32(7): 883-894. doi: 10.3879/j.issn.1000-0887.2011.07.011

平均间断有限元的强超收敛性及在Hamilton系统的应用

doi: 10.3879/j.issn.1000-0887.2011.07.011
基金项目: 国家自然科学基金资助项目(10771063)
详细信息
    作者简介:

    李灿华(1978- ),女,湖南南县人,博士生(联系人.Te:l+86-731-88872852;E-mai:lcan-huali827@hunnu.edu.cn).

  • 中图分类号: O242.21

Ultraconvergence for Averaging Discontinuous Finite Elements and Its Applications in Hamiltonian System

  • 摘要: 讨论了常微分方程初值问题的k次平均间断有限元.当k为偶数时,证明了在节点上的平均通量(间断有限元在节点上的左右极限的平均值)有2k+2阶最佳强超收敛性.对具有动量守恒的非线性Hamilton系统(如Schrdinger方程和Kepler系统),发现此类间断有限元在节点上是动量守恒的.这些性质被数值试验所证实.
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出版历程
  • 收稿日期:  2010-10-18
  • 修回日期:  2011-03-25
  • 刊出日期:  2011-07-15

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