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J4 ›› 2012, Vol. 47 ›› Issue (10): 89-96.

• 论文 • 上一篇    下一篇

非线性双曲方程Hermite型矩形元的高精度分析

王芬玲1,石东伟2   

  1. 1. 许昌学院数学与统计学院,  河南 许昌 461000; 2. 河南科技学院数学系, 河南 新乡 453000
  • 收稿日期:2012-05-02 出版日期:2012-11-20 发布日期:2012-10-26
  • 作者简介:王芬玲(1968- ),女,副教授,主要从事有限元方法及应用研究.Email: mathwfl@163.com
  • 基金资助:

    国家自然科学基金资助项目(10971203);河南省科技厅项目基金资助项目(122300410266);河南省教育厅自然科学基金资助项目(12A110021)

High analysis of Hermite-type rectangular element for nonlinear hyperbolic equation

WANG Fen-ling1, SHI Dong-wei2   

  1. 1. School of Mathematics and Statistics, Xuchang University, Xuchang 461000, Henan, China;
    2. Department of Mathematics, Henan Institute of Science and Technology,  Xinxiang 453000, Henan, China
  • Received:2012-05-02 Online:2012-11-20 Published:2012-10-26

摘要:

讨论了非线性双曲方程的Hermite型矩形有限元逼近。 利用该元的高精度分析、平均值理论和导数转移技巧得到了H1模意义下的超逼近性。 借助于插值后处理方法导出超收敛结果。最后,通过构造一个新的外推格式, 给出了与线性问题相同的四阶外推估计。

关键词: 非线性双曲方程; 超逼近和超收敛; Hermite型矩形元;外推

Abstract:

A Hermite-type rectangular finite element approximation is discussed for nonlinear hyperbolic equation. The superclose property in H1-norm is obtained by use of high accuracy analysis of the element, meanvalue theorem and the derivative transfering technique. The superconvergence result is derived with interpolation postprocessing method. Finally, the fourthorder extrapolation estimation which is as same as that of the linear problem is deduced through constructing a new extrapolation scheme.

Key words: nonlinear hyperbolic equation; superclose and superconvergence; Hermite-type rectangular element; extrapolation

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