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基于改进位移模式的二维有限元线法超收敛算法

唐义军 罗建辉

唐义军, 罗建辉. 基于改进位移模式的二维有限元线法超收敛算法[J]. 应用数学和力学, 2013, 34(8): 815-823. doi: 10.3879/j.issn.1000-0887.2013.08.005
引用本文: 唐义军, 罗建辉. 基于改进位移模式的二维有限元线法超收敛算法[J]. 应用数学和力学, 2013, 34(8): 815-823. doi: 10.3879/j.issn.1000-0887.2013.08.005
TANG Yi-jun, LUO Jian-hui. Algorithm of Super-Convergent in Two-Dimensional Finite Element of Lines Based on Improved Displacement Mode[J]. Applied Mathematics and Mechanics, 2013, 34(8): 815-823. doi: 10.3879/j.issn.1000-0887.2013.08.005
Citation: TANG Yi-jun, LUO Jian-hui. Algorithm of Super-Convergent in Two-Dimensional Finite Element of Lines Based on Improved Displacement Mode[J]. Applied Mathematics and Mechanics, 2013, 34(8): 815-823. doi: 10.3879/j.issn.1000-0887.2013.08.005

基于改进位移模式的二维有限元线法超收敛算法

doi: 10.3879/j.issn.1000-0887.2013.08.005
基金项目: 湖南省自然科学基金资助项目(08JJ3011)
详细信息
    作者简介:

    唐义军(1977—),男,湖南人,博士生,从事结构工程研究(通讯作者.E-mail: yijuntang168@163.com);罗建辉(1957—)男,湖南人,教授(E-mai:luojianhui@hnu.edu.cn).

  • 中图分类号: O241.82; O302

Algorithm of Super-Convergent in Two-Dimensional Finite Element of Lines Based on Improved Displacement Mode

  • 摘要: 提出了基于改进位移模式的二维有限元线法超收敛算法.利用单元内部需满足平衡方程的条件,推导了超收敛计算的解析公式的显式,即将高阶有限元线法解的位移模式用常规有限元线法解的位移模式表示.用常规有限元线法解的位移模式与高阶有限元线法解的位移模式之和构造新的位移模式,基于线性形函数,采用变分形式推导了有限元线法求解的修正的常微分方程组.该算法在前和后处理同时使用超收敛计算公式,在原有试函数的基础上,增加了高阶试函数.使得单元内平衡方程的残差减少,从而达到提高精度的目标.对于二维Poisson方程问题,给出了有代表性的算例,结点和单元内的位移、导数的收敛精度得到了极大的提高.
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出版历程
  • 收稿日期:  2013-01-10
  • 修回日期:  2013-06-25
  • 刊出日期:  2013-08-15

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