Anisotropic conforming rectangular elements for elliptic problems of any order

In this paper two sets of CN−1 conforming rectangular elements for linear elliptic problems of order 2N, N⩾1, are presented. One is bi−(2N−1) element, well known bi-linear element and bi-cubic C1 element (Bogner–Fox–Schmit) correspond to N=1 and N=2, respectively. Another one is bi−2N element, well known bi-quadratic element corresponds to N=1. The anisotropic error estimates are proved by the Newton's formulas for Hermite interpolation in two dimension and the special properties of the divided differences with coincident knots presented in this paper.