An octahedral C2 macro-element

A macro-element of smoothness C2 is constructed on the split of an octahedron into eight tetrahedra. This new element complements those recently constructed on the Clough–Tocher and Worsey–Farin splits of a tetrahedron (cf. Alfeld, P., Schumaker, L.L., 2005a, 2005b). The octahedral element uses supersplines of degree thirteen, and provides optimal order of approximation of smooth functions.