Trivariate Local Lagrange Interpolation and Macro Elements of Arbitrary Smoothness - Brossura

Matt, Michael Andreas

Brossura

ISBN 10: 383482383X ISBN 13: 9783834823830

Casa editrice: Vieweg+Teubner Verlag, 2012

Riassunto

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.

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Informazioni sull?autore

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.

Dalla quarta di copertina

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.

Dettagli dell'edizione

• Editore: Vieweg+Teubner Verlag
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 383482383X
• ISBN 13: 9783834823830
• Rilegatura: Copertina flessibile
• Numero di pagine: 388
• Contatto del produttore: Springer-Verlag GmbH; customerservice@springernature.com; ; Tiergartenstraße 17; Heidelberg; Baden-Württemberg; 69121; Germania