线性插值误差的精细估计及在有限元方法中的应用

Some Intensive Estimations for Linear Interpolation and Application in Finite Element Method

本文考虑到三角形区域的特殊性 ,给出了三角形区域上线性插值以及整个区域Ω上分片线性插值误差的精细估计 .有别于一般Soblev空间插值估计 ,估计中的常系数不仅是存在的 ,而且具体给了出来 ,为有限元计算单元剖分提供了依据 .并且这种方法可推广到高次多项式插值估计 .

In this paper,we give some estimations about the linear interpolation in triangle element.Compared the known results,the constants in estimate expressions are not only exsist,but definit as well.We also point that this method can be applied to higher order polynomial interpolation.The results are helpful to finite element error estimation.In an example,before calaculating,we can select h so that discrete solution u h approximates true solution u satisfying ‖u-u h‖≤.