On the Shape of Tetrahedra from Bisection
نویسندگان
چکیده
We present a procedure for bisecting a tetrahedron T successively into an infinite sequence of tetrahedral meshes ¡Tü , ZTX , ST1, ... , which has the following properties: (1) Each mesh !Tn is conforming. (2) There are a finite number of classes of similar tetrahedra in all the ¿Tn , n > 0. (3) For any tetrahedron T? in ¿T" , n(T") > cxn(T), where n is a tetrahedron shape measure and cx is a constant. (4) <5(T?) < c2(l/2)"/3«5(T), where <J(T') denotes the diameter of tetrahedron T and c2 is a constant. Estimates of cx and c2 are provided. Properties (2) and (3) extend similar results of Stynes and Adler, and of Rosenberg and Stenger, respectively, for the 2-D case. The diameter bound in property (4) is better than one given by Kearfott.
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