一维三次单位分解有限元插值的最优误差估计  

Optimal error estimate for partition of unity finite element method interpolants of 3-degree in 1-dimension

作　　者：李蔚[1] 

机构地区：[1]浙江科技学院理学院,杭州310023

出　　处：《浙江科技学院学报》2012年第4期269-272,共4页Journal of Zhejiang University of Science and Technology

基　　金：浙江省教育厅科研计划项目(Y201120196)

摘　　要：推导了一维三次单位分解有限元插值的最优阶误差。用标准的分片线性有限元基函数作单位分解,根据相容性和局部逼近性构造了一个特殊的局部多项式逼近空间,从而得到了具有3阶再生性的单位分解有限元插值格式;再应用Taylor展开及平均多项式插值理论推导插值误差估计。结果表明,误差估计阶比局部逼近阶要高,因而是最优的。Optimal error estimate for partition of unity finite element method （PUFEM） interpolants of 3-degree in one dimension is provided. Using standard linear finite element base functions as partition of unity, a special polynomial local approximation space can be established according to the consistence and local approximation properties. And PUFEM interpolants with reproducing property of order 3 is constructed. Then the interpolation error estimation of PUFEM is given by applying various techniques of Taylor expansion and theories of average polynomials interpolation. The result shows that the error estimate has higher order than the local approximation and is optimal.

关 键 词：最优误差估计 单位分解有限元法 三次插值 局部逼近空间 

分 类 号：O241.82[理学—计算数学] O241.1[理学—数学]