Abstract
A macro-element of smoothness C 2 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.
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