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Optimality of a Gradient Bound for Polyhedral Wachspress Coordinates

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Curves and Surfaces (Curves and Surfaces 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9213))

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Abstract

In a recent paper with Gillette and Sukumar an upper bound was derived for the gradients of Wachspress barycentric coordinates in simple convex polyhedra. This bound provides a shape-regularity condition that guarantees the convergence of the associated polyhedral finite element method for second order elliptic problems. In this paper we prove the optimality of the bound using a family of hexahedra that deform a cube into a tetrahedron.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Oslo, PO Box 1053, Blindern, 0316, Oslo, Norway

    Michael S. Floater

Authors
  1. Michael S. Floater
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Correspondence to Michael S. Floater .

Editor information

Editors and Affiliations

  1. INRIA, Sophia Antipolis, Sophia Antipolis, France

    Jean-Daniel Boissonnat

  2. École Normale Supérieure, Paris, France

    Albert Cohen

  3. Arts Et Metiers ParisTech Lab de Sciences de l'Information, Paris, France

    Olivier Gibaru

  4. INSA de Rouen, LMI, Saint-Étienne-du-Rouvray, France

    Christian Gout

  5. Department of Mathematics, University of Oslo, Oslo, Norway

    Tom Lyche

  6. Université Joseph Fourier, Grenoble, France

    Marie-Laurence Mazure

  7. Department of Mathematics, Vanderbilt University, Nashville, Tennessee, USA

    Larry L. Schumaker

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Floater, M.S. (2015). Optimality of a Gradient Bound for Polyhedral Wachspress Coordinates. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2014. Lecture Notes in Computer Science(), vol 9213. Springer, Cham. https://doi.org/10.1007/978-3-319-22804-4_16

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  • DOI: https://doi.org/10.1007/978-3-319-22804-4_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22803-7

  • Online ISBN: 978-3-319-22804-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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