| 有限元逆估计不等式中常数因子的界定 |
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| 引用本文： | 谭佼,何文明.有限元逆估计不等式中常数因子的界定[J].温州大学学报(社会科学版),2009(3):7-13. |
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| 作者姓名： | 谭佼 何文明 |
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| 作者单位： | 温州大学数学与信息科学学院,浙江温州325035 |
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| 摘 要： | 讨论了n维k（n,k∈N）次有限元空间逆估计不等式右端常数因子的界定问题.针对n维k（n,k∈N）次有限元空间,采取n单体剖分,结合Pk型Lagrange插值基函数,利用条件极值和Matlab软件,提出了计算n维k次有限元空间中逆估计不等式右端常数因子下确界的一种通用方法.利用该方法,对二维k（1≤k≤4）次有限元空间中逆估计不等式右端常数因子的下确界进行了具体计算,并且得到了下确界C 2,k的具体数值为：C 2,1=12,C 2,2≈25.0664,C 2,3≈40.0206,C 2,4≈82.3844.
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| 关 键 词： | 有限元空间 逆估计不等式 常数因子 |
Bound of Constant Factor in the Estimated Inverse Inequality of the Finite Element Space |
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| TAN Jiao,HE Wenming.Bound of Constant Factor in the Estimated Inverse Inequality of the Finite Element Space[J].Journal of Wenzhou University Natural Science,2009(3):7-13. |
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| Authors: | TAN Jiao HE Wenming |
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| Institution: | (College of Mathematics and Information Science, Wenzhou University, Wenzhou, China 325035) |
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| Abstract: | The bound of constant factor appearing in the right side of the estimated inverse inequality in the k（k∈ N） finite element space over n（n∈ N） dimensional domains wais discussed. For the k（k∈ N） finite element space over n（n ∈ N） dimensional domains, a common and effective method to obtain the bound of the constant factor in the k（k ∈ N） finite element space over n（n∈ N） dimensional domains was proposed by using the subdivision of n monomer, the element of Lagrange Pk, which is used to structure the interpolation functions, the method of extremum with a condition which was proposed by Lagrange, and the software Matlab, which is used to solve the equations. Using this method to do specific calculating, the bound of the constant factors in the estimated inverse inequality of the k（k = 1,2,3,4） finite element space over two dimensional domains could be achieved. They are C2.1 =12, C2.2 =25.0664, C2.3 =40.0206 and C2.4 = 82.3844. |
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| Keywords: | Finite Element Space Estimated Inverse Inequality Constant Factor |
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