| 三维二次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. 三维二次有限元梯度最大模的超逼近[J]. 数学物理学报(A辑), 2006, 26(3): 458-466 |
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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，湖南师范大学数学与计算机科学学院 长沙 410081，长沙 410081 |
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| 基金项目： | 国家自然科学基金(10371038)资助 |
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| 摘 要： | 作者证明了在一致四面体剖分下三维二次有限元的第一型弱估计,并给出了三维导数离散Green函数的估计,由此得到了四面体二次元梯度最大模的超逼近．通过这个超逼近还可以获得四面体二次元梯度最大模的超收敛．
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| 关 键 词： | 有限元 四面体 超逼近 第一型弱估计 导数离散Green函数 |
| 文章编号： | 1003-3998(2006)03-458-09 |
| 收稿时间： | 2004-05-26 |
| 修稿时间： | 2005-08-19 |
Maximum-norm Superapproach of the Gradient for Quadratic Finite Elements in Three Dimensions |
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| Liu Jinghong,Zhu Qiding. Maximum-norm Superapproach of the Gradient for Quadratic Finite Elements in Three Dimensions[J]. Acta Mathematica Scientia, 2006, 26(3): 458-466 |
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| Authors: | Liu Jinghong Zhu Qiding |
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| Affiliation: | School of Mathematics and Computer Science, Hunan Normal University, Changsha ,410081 |
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| Abstract: | For a model elliptic boundary value problem in three dimensions the authors prove the weak estimate of the first type over uniform tetrahedral partitions of the domain, and give the estimate of the discrete derivative Green function, from which the authors can derive maximum-norm superapproach of the gradient for tetrahedral quadratic finite elements. Furthermore, utilizing this superapproach, the authors also obtain maximum-norm superconvergence of the gradient for tetrahedral quadratic finite elements. |
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| Keywords: | Finite elements Tetrahedron Superapproach Weak estimate of the first type Discrete derivative Green function. |
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