  In this paper, we construct a $C^2$ finite element based on the Clough-Tocher
subdivision. We use derivatives order up to two at the vertices and cross
boundary derivatives order up to two along the exterior edges of the triangle.
The centroid of the triangle is just evaluated. The interpolant used is
globally $C^2,$ has local support, is piecewise polynomial of degree less or
equal to 5.
