Trivariate Local Lagrange Interpolation and Macro Elements of Arbitrary Smoothness

Authors: Matt, Michael Andreas

  • 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

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About this book

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.

About the authors

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.

Table of contents (8 chapters)

  • Introduction

    Matt, Michael A.

    Pages 1-7

  • Preliminaries

    Matt, Michael A.

    Pages 9-47

  • Minimal determining sets for splines on partialWorsey-Farin splits

    Matt, Michael A.

    Pages 49-130

  • Local Lagrange interpolation by cubic C1 splines on type-4 cube partitions

    Matt, Michael A.

    Pages 131-160

  • Local Lagrange Interpolation with C2 splines of degree nine on arbitrary tetrahedral partitions

    Matt, Michael A.

    Pages 161-197

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-3-8348-2384-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $119.00
price for USA
  • ISBN 978-3-8348-2383-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Trivariate Local Lagrange Interpolation and Macro Elements of Arbitrary Smoothness
Authors
Copyright
2012
Publisher
Vieweg+Teubner Verlag
Copyright Holder
Springer Spektrum | Springer Fachmedien Wiesbaden
eBook ISBN
978-3-8348-2384-7
DOI
10.1007/978-3-8348-2384-7
Softcover ISBN
978-3-8348-2383-0
Edition Number
1
Number of Pages
XVI, 370
Number of Illustrations and Tables
85 b/w illustrations, 2 illustrations in colour
Topics