| 张量积二次长方体有限元梯度最大模的超逼近 |
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| 引用本文： | 刘经洪,朱起定.张量积二次长方体有限元梯度最大模的超逼近[J].计算数学,2005,27(3):267-276. |
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| 作者姓名： | 刘经洪 朱起定 |
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| 作者单位： | 湖南师范大学数学与计算机科学学院,长沙,410081;湖南师范大学数学与计算机科学学院,长沙,410081 |
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| 基金项目： | 国家自然科学基金资助项目（10371038）. |
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| 摘 要： | 对于某种三维椭圆边值问题，本文给出了长方体剖分下张量积二次长方体有限元的第一型弱估计以及离散导数Green函数的W^1，1半范估计，利用这两个估计本文获得了张量积二次长方体有限元梯度最大模的超逼近．进而，由超逼近也可以得到这种有限元梯度最大模的超收敛．
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| 关 键 词： | 有限元 长方体 超逼近 第一型弱估计 离散导数Green函数 |
| 收稿时间： | 2004-03-15 |
| 修稿时间： | 2004-03-15 |
MAXIMUM-NORM SUPERAPPROXIMATION OF THE GRADIENT FOR THE TENSOR-PRODUCT QUADRATIC RECTANGULAR PARALLELEPIPED FINITE ELEMENT |
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| Liu Jinghong,ZHU Qiding.MAXIMUM-NORM SUPERAPPROXIMATION OF THE GRADIENT FOR THE TENSOR-PRODUCT QUADRATIC RECTANGULAR PARALLELEPIPED FINITE ELEMENT[J].Mathematica Numerica Sinica,2005,27(3):267-276. |
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| Authors: | Liu Jinghong ZHU Qiding |
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| Institution: | Liu Jinghong Zhu Qiding (School of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China) |
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| Abstract: | For an elliptic boundary value problem in three dimensions this paper will give the weak estimate of the first type for tensor-product quadratic rectangular parallelepiped elements and the estimate for the W1,1 seminorm of the discrete derivative Green's function over rectangular parallelepiped partitions of the domain, from which this paper will obtain maximum-norm superapproximation of the gradient for the tensor-product quadratic rectangular parallelepiped finite element. Furthermore, by this superapproximation, maximum-norm superconvergence of the gradient for the finite element can also be obtained. |
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| Keywords: | finite elements rectangular parallelepiped superapproximation weak estimate of the first type discrete derivative Green's function |
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