| 二阶Dirichlet问题的三维等参元逼近及其数值积分格式 |
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| 引用本文： | 张斐然,陈绍春.二阶Dirichlet问题的三维等参元逼近及其数值积分格式[J].计算数学,2008,30(2):183-194. |
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| 作者姓名： | 张斐然 陈绍春 |
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| 作者单位： | 1. 商丘师院数学系,河南,商丘,476000
2. 郑州大学数学系,郑州,450052 |
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| 摘 要： | 本文研究了求解三维二阶Drichlet问题的四面体等参元逼近格式.基于对等参变换的细致估计,证明了格式的收敛性,并得到了H~1-误差的最优估计.为简化等参元的复杂计算,本文还构造了一种简单的数值积分格式,并证明了其收敛性.
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| 关 键 词： | 三维椭圆型方程 等参有限元 等参变换 数值积分 |
| 修稿时间： | 2007年3月30日 |
THE APPROXIMATION BY 3-DIMENSIONAL ISOPARAMETRIC ELEMENT AND A KIND OF NUMERICAL INTEGRATION FORMAT OF 2ND ORDER DIRICHLET PROBLEM |
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| Zhang Feiran,Chen Shaochun.THE APPROXIMATION BY 3-DIMENSIONAL ISOPARAMETRIC ELEMENT AND A KIND OF NUMERICAL INTEGRATION FORMAT OF 2ND ORDER DIRICHLET PROBLEM[J].Mathematica Numerica Sinica,2008,30(2):183-194. |
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| Authors: | Zhang Feiran Chen Shaochun |
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| Institution: | Zhang Feiran (Department of Mathematics,Shangqiu Teachers Colloege,Shangqiu 476000,Henan,China) Chen Shaochun (Department of Mathematics,Zhengzhou University,Zhengzhou 450052,China) |
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| Abstract: | An approximation format of tetrahedral isoparametric element for solving the 3-dimensional 2-order Dirichlet problem is presented in this paper first,then based on the optical estima- tion of isoparametric transformation,we prove the convergence of the format given,obtain the optical H~1 estimate error.In order to simplify the complex computing of isoparametric element,we also construct a simple kind of numerical integration format,and its convergence is proved later. |
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| Keywords: | 3-dimensional ellipse equation isoparametric finite element isoparametric transformation numerical integration |
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