A New Kind of Trivariate C 1 Macro - ElementMing
نویسنده
چکیده
We propose a construction of a trivariate C 1 macro-element over a special tetrahedral partition and compare our construction with known C 1 macro-elements which are summarized in this paper. Also, we propose an improvement of the Alfeld construction of a C 1 quintic macro-element such that the new scheme is able to reproduce all polynomials of total degree 5. x1. Introduction The study of trivariate spline functions was pioneered by Zeni cek, LeM ehaut e, Alfeld, Worsey, Farin among others. See references Zeni cek'73], LeMehaute'84], Alfeld'84], Worsey and Farin'87], and Worsey and Piper'88]. Most of these results involve the construction of trivariate C 1 macro-elements over a tetrahedral partition or a reenement of. They are generalizations of the well-known bivariate C 1 quintic Argyris element, C 1 Clough-Tocher element, or C 1 quadratic Powell-Sabin element. In this paper we shall present a new kind of trivariate C 1 macro-element which is generalized from the bivariate C 1 cubic FVS elements ((Fraejis en Veubeke'65] and Sander'64]). Such an element has not been presented in the literature so far to the best of our knowledge. The new C 1 macro-element ooers several advantages over the existing C 1 macro-elements cited above. (See Remarks 4.1{4.3 and 4.10.) To describe the new macro-element, we begin with a special tetrahedral par
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