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Published in:
2012 | OriginalPaper | Chapter
Macro-elements of arbitrary smoothness over the Worsey-Farin split of a tetrahedron
Author : Michael A. Matt
Published in: Trivariate Local Lagrange Interpolation and Macro Elements of Arbitrary Smoothness
Publisher: Vieweg+Teubner Verlag
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In this chapter we describe the C
r
macro-elements based on the Worsey- Farin split of a tetrahedron (see Definition 2.7) by Matt [66]. In section 8.1, we review the minimal conditions for the degree of polynomials and the degree of supersmoothness for constructing C
r
macro-elements over the Worsey-Farin split. In the following section 8.2, we investigate minimal determining sets for C
r
macro-elements defined on the Worsey-Farin split of tetrahedra. In the next section, we illustrate these minimal determining sets with some examples to ease their understanding. In section 8.4, we examine nodal minimal determining sets for the C
r
splines considered in this chapter. Finally, in section 8.5, a Hermite interpolant set for C
r
splines based on the Worsey-Farin split is constructed. Moreover, it is shown that the interpolation yields optimal approximation order.