Trivariate Local Lagrange Interpolation and Macro Elements of Arbitrary Smoothness

1. Auflage 2012
ISBN: 978-3-8348-2383-0
Verlag: Vieweg+Teubner Verlag

Buch, Englisch, 370 Seiten, Format (B × H): 148 mm x 210 mm, Gewicht: 500 g

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 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 Cr macro-elements are constructed over the Clough-Tocher split of a triangle, which are more variable than those in the literature.

Zielgruppe

Research

Autoren/Hrsg.

Matt, Michael Andreas

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Lagrange Interpolation on Type-4 Partitions.- Trivariate Lagrange Interpolation with C² Splines.-  Cr Macro-Element over the Clough-Tocher Split.- Cr Macro-Element over the Alfeld Split.- Cr Macro-Element over the Worsey Farin Split.

Über Autor(innen)

Matt, Michael Andreas
Michael A. Matt studied multivariate spline theory at the University of Mannheim, especially macro-element methods and Lagrange interpolation. He currently works at the Institute for Mathematics at the University of Mannheim.

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.