多边形单元Wachspress插值的误差估计

Wachspress插值是多边形单元上的一种有理函数形式的插值格式。利用Wachspress插值可以建立多边形单元的形函数，得到求解偏微分方程边值问题的多边形有限元方法。本文对多边形单元wachspress插值进行了分析，给出了Wachspress插值形函数计算的简化公式。利用所得到的Wachspress插值形函数的简化公式，可以方便地编制计算程序。利用wachspress插值形函数的性质和二元函数的Taylor展开式的向量形式，给出了wachspress插值的误差估计不等式。Wachspress插值的误差估计不等式表明，Wachspress插值的插值误差随着多边形单元尺寸的减小而减少。

Error estimation of Wachspress interpolation on polygonal elements

The shape functions of Wachspress interpolation is one of the rational function forms of a polygon. Using Wachspress interpolation function as shape functions of polygonal element, the polygonal finite element method for solving boundary value problems of partial differential equation is introduced. In this paper, the simplified formulations of Wachspress interpolation shape function are given. Using the properties of shape functions of Wachspress interpolation and the vector form of bivaxiate Taylor expression, the error estimation of Wachspress interpolation within polygonal element is presented. The error estimation inequation of Wachspress interpolation indicates that the error of Wachspress interpolation decreases with the reduction of polygonal element size.