Title
Trivariate Local Lagrange Interpolation and Macro Elements of Arbitrary Smoothness,Used
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Michael A. Matt constructs two trivariate local Lagrange interpolation methods which yield optimal approximation order and Cr macroelements based on the Alfeld and the WorseyFarin split of a tetrahedral partition. The first interpolation method is based on cubic C1 splines over type4 cube partitions, for which numerical tests are given. The second is the first trivariate Lagrange interpolation method using C2 splines. It is based on arbitrary tetrahedral partitions using splines of degree nine. The author constructs trivariate macroelements based on the Alfeld split, where each tetrahedron is divided into four subtetrahedra, and the WorseyFarin split, where each tetrahedron is divided into twelve subtetrahedra, of a tetrahedral partition. In order to obtain the macroelements based on the WorseyFarin split minimal determining sets for Cr macroelements are constructed over the CloughTocher split of a triangle, which are more variable than those in the literature.
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