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| Lagrange四边形单位分解有限元法的最优误差分析 | |
| 引用本文： | 李蔚,黄云清,周佳立.Lagrange四边形单位分解有限元法的最优误差分析[J].数学的实践与认识,2012,42(12):249-258. |
| 作者姓名： | 李蔚 黄云清 周佳立 |
| 作者单位： | 1. 浙江科技学院理学院,浙江杭州,310023 2. 湘潭大学数学与计算科学学院,湖南湘潭,411105 3. 浙江工业大学数学系,浙江杭州,310023 |
| 摘 要： | 用构造最优局部逼近空间的方法对Lagrange型四边形单位分解有限元法进行了最优误差分析.单位分解取Lagrange型四边形上的标准双线性基函数,构造了一个特殊的局部多项式逼近空间,给出了具有2阶再生性的Lagrange型四边形单位分解有限元插值格式,从而得到了高于局部逼近阶的最优插值误差. |
| 关 键 词： | 最优误差估计 单位分解有限元法 Lagrange四边形 |
Optimal Error Estimates for Partition of Unity Finite Element Method on Lagrange Rectangle |
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| LI Wei , HUANG Yun-qing , ZHOU Jia-li.Optimal Error Estimates for Partition of Unity Finite Element Method on Lagrange Rectangle[J].Mathematics in Practice and Theory,2012,42(12):249-258. | |
| Authors: | LI Wei HUANG Yun-qing ZHOU Jia-li |
| Institution: | 1.School of Science,Zhejiang University of Science and Technology,Hangzhou 310023,China) (2.Institute for Computational and Applied Mathematics,Xiangtan University,Xiangtan 411105,China) (3.Department of Mathematics,Zhejiang University of Technology,Hangzhou 310023,China) |
| Abstract: | In this paper,by constructing a optimal local approximation space,we investigate optimal error estimates for partition of unity finite element method(PUFEM)on Lagrange rectangle.Using standard base functions defined on bilinear Lagrange rectangle as partition of unity,a special polynomial local approximation space is established,then PUFEM interpolants with reproducing property of order 2 is constructed.Thereby we derive the optimal error estimates of higher order than the local approximations for PUFEM interpolants. |
| Keywords: | optimal error estimate partition of unity finite element method Lagrange rectangle |
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