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山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (4): 90-98.doi: 10.6040/j.issn.1671-9352.0.2015.154

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拟线性黏弹性方程一个新的H 1-Galerkin混合有限元分析

刁群1,石东洋2   

  1. 1.平顶山学院数学与信息科学学院, 河南 平顶山 467000;2.郑州大学数学与统计学院, 河南 郑州 450001
  • 收稿日期:2015-04-14 出版日期:2016-04-20 发布日期:2016-04-08
  • 作者简介:刁群(1979— ), 女, 硕士, 讲师, 研究方向为有限元方法及其应用. E-mail:diaoqun.happy@163.com
  • 基金资助:
    国家自然科学基金资助项目(11271340)

New H 1-Galerkin mixed finite element analysis for quasi-linear viscoelasticity equation

DIAO Qun1, SHI Dong-yang2   

  1. 1. School of Mathematics and Information Science, Pingdingshan University, Pingdingshan 467000, Henan, China;
    2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, Henan, China
  • Received:2015-04-14 Online:2016-04-20 Published:2016-04-08

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摘要： 利用不完全双二次元Q-2和一阶BDFM元, 对拟线性黏弹性方程构造了一个新的H 1-Galerkin混合元模式。通过Bramble-Hilbert引理, 证明了单元所对应的插值算子一个新的高精度结果。 进一步地, 在半离散和一个二阶全离散格式下, 分别导出了原始变量u在H 1-模和中间变量(→overp)在 H(div)-模意义下的超逼近性质。

关键词: 拟线性黏弹性方程, Bramble-Hilbert引理, 超逼近, H 1-Galerkin混合有限元方法, 半离散和全离散格式

Abstract: A new H 1-Galerkin mixed finite element pattern for quasi-linear viscoelasticity equation is constructed using incomplete biquadratic element Q-2 and first order BDFM element. Through Bramble-Hilbert lemma, a newhigh precision results of interpolation operators corresponding to unit are proved. Further, the superclose properties for the primitive variables u in H 1-norm and the intermediate variable (→overp) in H(div)-norm are obtained respectively in semi-discrete and fully discrete schemes.

Key words: quasi-linear viscoelasticity equation, H 1-Galerkin mixed finite element method, superclose, semi-discrete and fully discrete schemes, Bramble-Hilbert lemma

中图分类号: 

  • O242.21
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