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强阻尼波动方程的H1-Galerkin混合有限元超收敛分析

石东洋, 唐启立, 董晓靖   

  1. 郑州大学数学系, 郑州 450001
  • 收稿日期:2012-03-14 出版日期:2012-08-15 发布日期:2012-08-16
  • 基金资助:

    国家自然科学基金项目(10971203,11101384)和高等学校博士学科点专项科研基金项目(20094101110006)资助课题.

石东洋, 唐启立, 董晓靖. 强阻尼波动方程的H1-Galerkin混合有限元超收敛分析[J]. 计算数学, 2012, 34(3): 317-328.

Shi Dongyang, Tang Qili, Dong Xiaojing. SUPERCONVERGENCE ANALYSIS OF H1-GALERKIN MIXED FINITE ELEMENT METHOD FOR STRONGLY DAMPED WAVE EQUATIONS[J]. Mathematica Numerica Sinica, 2012, 34(3): 317-328.

SUPERCONVERGENCE ANALYSIS OF H1-GALERKIN MIXED FINITE ELEMENT METHOD FOR STRONGLY DAMPED WAVE EQUATIONS

Shi Dongyang, Tang Qili, Dong Xiaojing   

  1. Department of Mathematics, Zhengzhou University, Zhengzhou 450001, China
  • Received:2012-03-14 Online:2012-08-15 Published:2012-08-16
研究了强阻尼波动方程的H1-Galerkin混合有限元方法的超收敛性. 借助于协调线性三角形元已有的分析估计式, 直接利用插值算子代替原始变量 u 的 Ritz 投影和应力变量 p 的 Ritz-Volterra 投影,对半离散和全离散格式, 得到了uH1(Ω) 模和 p 在 H(div;Ω) 模意义下比以往文献高一阶的超逼近和超收敛结果.
In this paper, the superconvergence analysis of H1-Galerkin mixed finite element method for strongly damped wave equations is studied. By virtue of the technique of interpolation operator instead of Ritz projection of the original variable u and Ritz-Volterra projection of the stress variable p, the superclose and superconvergence results in H1(Ω) norm for u and H(div;Ω) norm for p for both semidiscrete and fully discrete schemes are derived through applying some error estimates of conforming linear triangular finite element.

MR(2010)主题分类: 

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