Trivariate Local Lagrange Interpolation and Macro Elements of Arbitrary Smoothness (PDF)

Name: Trivariate Local Lagrange Interpolation and Macro Elements of Arbitrary Smoothness
Brand: Vieweg+Teubner Verlag
SKU: 43011196
Price: 54.99 EUR
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(Sprache: Englisch)

Autor: Michael Andreas Matt

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Trivariate Local Lagrange Interpolation and Macro Elements of Arbitrary Smoothness, Michael Andreas Matt

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Michael A. Matt constructs two trivariate local Lagrange interpolation methods which yield optimal approximation order and Cr macro-elements based on the Alfeld and the Worsey-Farin split of a tetrahedral partition. The first interpolation method is based...

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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 C¹ splines over type-4 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 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.

Autoren-Porträt von Michael Andreas Matt

Dr. Michael A. Matt completed his doctoral thesis under the supervision of Prof. Dr. Günther Nürnberger at the Chair of Mathematics IV, University of Mannheim.