Definiteness of Shape Function of Isoparametric Element for Many Nodes

This paper is the analysis for the shape function of the higher order elements, according to the definition of the shape function strictly. In this article we quoted the cover lines and the cover areas, including also the circular are and the circular ball. It tells detail steps for the shape function of the different elements, which are simple and can save times, it is better than some function articles about the shape defined by the interpolation.