A scheme for rational interpolation on a quadrilateral of class C2

Let Q be a partition of a polygonal domain of the plan into convexe quadrilaterals. Given a regular function f, we construct a function Pif is an element of C-2(Ohm), interpolating position values and derivatives of f up of order 2 at vertices of Q. On each quadrilateral Q is an element of Q, Pif(\Q) is a finite element obtained from a polynomial scheme of FVS type by adding some rational functions.