Details
Trivariate Local Lagrange Interpolation and Macro Elements of Arbitrary Smoothness
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53,49 € |
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| Verlag: | Vieweg & Teubner |
| Format: | |
| Veröffentl.: | 10.05.2012 |
| ISBN/EAN: | 9783834823847 |
| Sprache: | englisch |
| Anzahl Seiten: | 370 |
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Beschreibungen
<p>Michael A. Matt constructs two trivariate local Lagrange interpolation methods which yield optimal approximation order and C<sup>r</sup> macro-elements based on the Alfeld and the Worsey-Farin split of a tetrahedral partition. The first interpolation method is based on cubic C<sup>1</sup> splines over type-4 cube partitions, for which numerical tests are given. The second is the first trivariate Lagrange interpolation method using C<sup>2</sup> 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<sup>r</sup> macro-elements are constructed over the Clough-Tocher split of a triangle, which are more variable than those in the literature.</p>
<p>Lagrange Interpolation on Type-4 Partitions.- Trivariate Lagrange Interpolation with C² Splines.- C<sup>r</sup> Macro-Element over the Clough-Tocher Split.- C<sup>r</sup> Macro-Element over the Alfeld Split.- C<sup>r</sup> Macro-Element over the Worsey Farin Split.</p>
<p>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.</p>
<p>Michael A. Matt constructs two trivariate local Lagrange interpolation methods which yield optimal approximation order and C<sup>r</sup> macro-elements based on the Alfeld and the Worsey-Farin split of a tetrahedral partition. The first interpolation method is based on cubic C<sup>1</sup> splines over type-4 cube partitions, for which numerical tests are given. The second is the first trivariate Lagrange interpolation method using C<sup>2</sup> 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<sup>r</sup> macro-elements are constructed over the Clough-Tocher split of a triangle, which are more variable than those in the literature.</p>
Two trivariate local Lagrange interpolation methods are constructed which yield optimal approximation order and Cr macro-elements based on the Alfeld and the Worsey-Farin split of a tetrahedral partition
<p>Michael A. Matt constructs two trivariate local Lagrange interpolation methods which yield optimal approximation order and C<sup>r</sup> macro-elements based on the Alfeld and the Worsey-Farin split of a tetrahedral partition. The first interpolation method is based on cubic C<sup>1</sup> splines over type-4 cube partitions, for which numerical tests are given. The second is the first trivariate Lagrange interpolation method using C<sup>2</sup> 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<sup>r</sup> macro-elements are constructed over the Clough-Tocher split of a triangle, which are more variable than those in the literature.</p>
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