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

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

湖南师范大学数学与计算机科学学院,长沙 410081

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
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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

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

College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, P. R. China

摘要

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．
- 平均间断有限元 /
- 强超收敛 /
- Hamilton系统 /
- 动量守恒
Abstract: The k-degree averaging discontinuous finite element solution for the initial value problem of ordinary differential equations was discussed. When k waseven, it was proved that the averaging numerical flux (the average of left and right lmiits for discon tinuous finite element at nodes) had the optmial order ultraconvergence 2k + 2. For non linear Hamiltonian systems (e. g., S chrêdinger equation and Kepler system) with momentum conservation, it was found that the discon tinuous finite element methods preserve momentum at nodes. These properties were confirmed by numerical expermients.
- averaging discontinuous finite element /
- ultraconvergence /
- Hamiltonian system /
- momentum conservation

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参考文献(16)

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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

doi: 10.3879/j.issn.1000-0887.2011.07.011

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).

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

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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

doi: 10.3879/j.issn.1000-0887.2011.07.011

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).

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出版历程

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

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出版历程

目录

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).