Anisotropic conforming rectangular elements for elliptic problems of any order

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