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

Clough-Tocher scheme, piecewise polynomial, finite element.