Rational finite elements of class over a quadrangulation

In this paper we give a constructive method for rational C k finite element method in R 2 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 C 1 case and the C 2 case.