Let P be some partition of a planar polygonal domain Ω into quadrilaterals. Given a smooth function u, we construct piecewise polynomial functions υ ∈ C ρ (Ω) of degree n = 3ρ for ρ odd, and n = 3ρ + 1 for ρ even on a subtriangulation τ 4 of P . The latter is obtained by drawing diagonals in each Q ∈ P , and υ|Q is a composite quadrilateral finite element generalizing the classical C 1 cubic Fraeijs de Veubeke and Sander (or FVS) quadrilateral. The function υ interpolates the derivatives of u up to order ρ + [ρ/2] at the vertices of P . Polynomial degrees obtained in this way are minimal in the family of interpolation schemes based on finite elements. Classification (1991): 41A15, 41A05, 65D07, 65D051 65N30 Mathematics Subject