三角形单元上二次Lagrange型插值多项式与被插函数的误差估计

The error estimates of 2-degree Lagrange's interpolation for triangular element

冯康在文［２］中证明了三角形单元Ｃ上一次Ｌａｇｒａｎｇｅ型插值函数Ｕ与被插函数ｕ的误差估计为：这里θ为三角单元Ｃ的最大内角，ｈ为最大边长．本文将该结果推广至二次Ｌａｇｒａｎｇｅ型插值多项式。并得到了相应的误差估计。

This paper generalizes the results of error estimates in [2]. The error estimates of 1-degree Lagrange's interpolation for triangular element is generalized to one of 2 - degree Lagrange's interpolation. This paper proves the error estimates of 1 - degree detivative for function and its interpolating function under some conditions.