An octahedral C2 macro-element

Authors:
Ming-Jun Lai;Alan Le Méhauté;Tatyana Sorokina
Affiliations:
Department of Mathematics, The University of Georgia, Athens, GA 30602, USA;Department of Mathematics, The University of Nantes, F.44322 Nantes, France;Department of Mathematics, The University of Georgia, Athens, GA 30602, USA
Venue:
Computer Aided Geometric Design
Year:
2006

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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.