| OPTIMAL ERROR ESTIMATES OF THE PARTITION OF UNITY METHOD WITH LOCAL POLYNOMIAL APPROXIMATION SPACES |
| |
| 作者姓名： | Yun-qing Huang Wei Li Fang Su |
| |
| 作者单位： | Yun-qing Huang，Hunan Key Laboratory for Compulation and Simulation in Science and Engineering，Institute for Computational and Applied Mathematics. Xiangtan University，Xiangtan 411105，ChinaWei Li;Fang Su，Department of Computational Science，Xiangtan University，Xiangtan 411105，China |
| |
| 基金项目： | This work was subsidized by the National Basic Research Program of China under the grant 2005CB321701，the Doctoral Program Funds of the Statc Education Ministry |
| |
| 摘 要： | In this paper, we provide a theoretical analysis of the partition of unity finite elementmethod (PUFEM), which belongs to the family of meshfree methods. The usual erroranalysis only shows the order of error estimate to the same as the local approximations12].Using standard linear finite element base functions as partition of unity and polynomials aslocal approximation space, in 1-d case, we derive optimal order error estimates for PUFEMinterpolants. Our analysis show that the error estimate is of one order higher than thelocal approximations. The interpolation error estimates yield optimal error estimates forPUFEM solutions of elliptic boundary value problems.
|
| 关 键 词： | 统一有限元法间隔 误差估计 局部逼近 非线性有限元基本函数 |
| 收稿时间： | 2006-03-01 |
| 修稿时间： | 2006-03-01 |
OPTIMAL ERROR ESTIMATES OF THE PARTITION OF UNITY METHOD WITH LOCAL POLYNOMIAL APPROXIMATION SPACES |
| |
| Yun-qing Huang Wei Li Fang Su.OPTIMAL ERROR ESTIMATES OF THE PARTITION OF UNITY METHOD WITH LOCAL POLYNOMIAL APPROXIMATION SPACES[J].Journal of Computational Mathematics,2006,24(3):365-372. |
| |
| Authors: | Yun-qing;Huang;Wei;Li;Fang;Su |
| |
| Abstract: | In this paper, we provide a theoretical analysis of the partition of unity finite element method (PUFEM), which belongs to the family of meshfree methods. The usual error analysis only shows the order of error estimate to the same as the local approximations12]. Using standard linear finite element base functions as partition of unity and polynomials as local approximation space, in 1-d case, we derive optimal order error estimates for PUFEM interpolants. Our analysis show that the error estimate is of one order higher than the local approximations. The interpolation error estimates yield optimal error estimates for PUFEM solutions of elliptic boundary value problems. |
| |
| Keywords: | Meshless methods Partition of unity finite element method(PUFEM) Error estimate |
| 本文献已被 CNKI 维普 等数据库收录！ |
