Rational finite elements of class Ck over a quadrangulation

In this paper we give a constructive method for rational Ck finite element method in R2 for quadrilateral. For k⩾2, the usual polynomials splines require some supersmoothness at the vertices of the quadrilateral, even when dealing with macro-elements. This is no more a requirement for our rational approach. The process of the construction is illustrated with the help of two examples namely the C1 case and the C2 case.