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Stable Splitting of Bivariate Splines Spaces by Bernstein-Bézier Methods

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Book cover Curves and Surfaces (Curves and Surfaces 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6920))

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Abstract

We develop stable splitting of the minimal determining sets for the spaces of bivariate C 1 splines on triangulations, including a modified Argyris space, Clough-Tocher, Powell-Sabin and quadrilateral macro-element spaces. This leads to the stable splitting of the corresponding bases as required in Böhmer’s method for solving fully nonlinear elliptic PDEs on polygonal domains.

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References

  1. Böhmer, K.: On finite element methods for fully nonlinear elliptic equations of second order. SIAM J. Numer. Anal. 46(3), 1212–1249 (2008)

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Strathclyde, Glasgow, United Kingdom

    Oleg Davydov & Abid Saeed

Authors
  1. Oleg Davydov
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  2. Abid Saeed
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Editor information

Editors and Affiliations

  1. INRIA Sophia-Antipolis, 2004 Route des Lucioles, BP 93, 06902, Sophia Antipolis, France

    Jean-Daniel Boissonnat

  2. Laboratoire LJK, University Joseph Fourier, BP 53, 38420, Grenoble Cedex 9, France

    Patrick Chenin

  3. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 4, Place Jussieu, 75005, Paris, France

    Albert Cohen

  4. Laboratoire de Mathématiques, INSA Rouen, Avenue de l’Université, 76800, St. Etienne du Rouvray, France

    Christian Gout

  5. University of Oslo, DMA, Blindern, P.O.Box 1053, 0316, Oslo, Norway

    Tom Lyche

  6. Laboratoire LJK, Université Joseph Fourier, BP 53, 38041, Grenoble Cedex 9, France

    Marie-Laurence Mazure

  7. Department of Mathematics, Vanderbilt University, 37240, Nashville, TN, USA

    Larry Schumaker

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Davydov, O., Saeed, A. (2012). Stable Splitting of Bivariate Splines Spaces by Bernstein-Bézier Methods. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2010. Lecture Notes in Computer Science, vol 6920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27413-8_14

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  • DOI: https://doi.org/10.1007/978-3-642-27413-8_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27412-1

  • Online ISBN: 978-3-642-27413-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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