FINITE ELEMENT DERIVATIVE INTERPOLATION RECOVERY TECHNIQUE AND SUPERCONVERGENCE

Tie Zhang; Shuhua Zhang

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FINITE ELEMENT DERIVATIVE INTERPOLATION RECOVERY TECHNIQUE AND SUPERCONVERGENCE

机译：有限元导数插值恢复技术和超收敛

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A new finite element derivative recovery technique is proposed by using the polynomial interpolation method. We show that the recovered derivatives possess supercon-vergence on the recovery domain and ultraconvergence at the interior mesh points for finite element approximations to elliptic boundary problems. Compared with the well-known Z-Z patch recovery technique, the advantage of our method is that it gives an explicit recovery formula and possesses the ultraconvergence for the odd-order finite elements. Finally, some numerical examples are presented to illustrate the theoretical analysis.

机译：利用多项式插值法提出了一种新的有限元导数恢复技术。我们表明，对于椭圆边界问题的有限元逼近，回收的导数在恢复域上具有超收敛性，并且在内部网格点具有超收敛性。与众所周知的Z-Z补丁恢复技术相比，我们的方法的优点在于它给出了一个明确的恢复公式，并且对奇数阶有限元具有超收敛性。最后，给出一些数值例子来说明理论分析。

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来源
《Applications of Mathematics》 |2011年第6期|p.513-531|共19页
作者
Tie Zhang; Shuhua Zhang;
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作者单位

Department of Mathematics, Northeastern University, Shenyang 110004, P.R.China;

Department of Mathematics, Tianjin University of Finance and Economics, Tianjin 300222, P.R.China;

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原文格式 PDF
正文语种 eng
中图分类
关键词
finite element method; derivative recovery technique; superconvergence and ultraconvergence;

机译：有限元法导数恢复技术超收敛和超收敛;

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2. DERIVATIVE SUPERCONVERGENCE OF LINEAR FINITE ELEMENTS BY RECOVERY TECHNIQUES [J] . Tie Zhang, Changjun Li, Yiyong Nie Dynamics of continuous, discrete & impulsive systems, Series A. Mathematical analysis . 2004,第5a6期

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8. Study of Superconvergence by a Computer-Based Approach: Superconvergence of theGradient of the Displacement, The Strain and Stress in Finite Element Solutions for Plane Elasticity [R] . Babuska, I., Strouboulis, T., Upadhyay, C. S., 1994

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FINITE ELEMENT DERIVATIVE INTERPOLATION RECOVERY TECHNIQUE AND SUPERCONVERGENCE

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