Two tetrahedral C1 cubic macro elements

We propose two tetrahedral C-1 Cubic macro elements that are constructed locally oil one tetrahedron without any knowledge of the geometry of neighboring tetrahedra. Among such geometrically unconstrained local polynomial tetrahedral C-1 schemes requiring only first order derivative data, our macro elements have the smallest number of coefficients. The resulting macro element spaces are stable and provide full approximation power. We give explicit formulae that call be used to implement our schemes. (C) 2008 Elsevier Inc. All rights reserved.