Matt, Michael Andreas
2012, XVI, 370p. 87 illus., 2 illus. in color.
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Michael A. Matt constructs two trivariate local Lagrange interpolation methods which yield optimal approximation order and C^{r} macro-elements based on the Alfeld and the Worsey-Farin split of a tetrahedral partition. The first interpolation method is based on cubic C^{1} splines over type-4 cube partitions, for which numerical tests are given. The second is the first trivariate Lagrange interpolation method using C^{2} splines. It is based on arbitrary tetrahedral partitions using splines of degree nine. The author constructs trivariate macro-elements based on the Alfeld split, where each tetrahedron is divided into four subtetrahedra, and the Worsey-Farin split, where each tetrahedron is divided into twelve subtetrahedra, of a tetrahedral partition. In order to obtain the macro-elements based on the Worsey-Farin split minimal determining sets for C^{r} macro-elements are constructed over the Clough-Tocher split of a triangle, which are more variable than those in the literature.
Content Level » Research
Keywords » Finite Elements - Lagrange Interpolation - Macro-Element Methods - Splintinterpolation - Theory of Approximation
Related subjects » Applications
Lagrange Interpolation on Type-4 Partitions.- Trivariate Lagrange Interpolation with C² Splines.- C^{r} Macro-Element over the Clough-Tocher Split.- C^{r} Macro-Element over the Alfeld Split.- C^{r} Macro-Element over the Worsey Farin Split.
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