Stable splitting of bivariate spline spaces by Bernstein-Bézier methods

Oleg Davydov, Abid Saeed

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

5 Citations (Scopus)
31 Downloads (Pure)

Abstract

We develop stable splitting of the minimal determining sets for the spaces of bivariate C1 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.
Original languageEnglish
Title of host publicationCurves and Surfaces
Subtitle of host publicationLecture Notes in Computer Science
EditorsJ.D. Boissonnat et al
PublisherSpringer-Verlag
Pages220-235
Number of pages16
Volume6920
ISBN (Print)978-3-642-27412-1
DOIs
Publication statusPublished - 2012
EventCurves and Surfaces - 7th International Conference - Avignon, France
Duration: 24 Jun 201230 Jun 2012

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
ISSN (Print)0302-9743

Conference

ConferenceCurves and Surfaces - 7th International Conference
CountryFrance
CityAvignon
Period24/06/1230/06/12

Fingerprint

Bivariate Splines
Nonlinear Elliptic PDE
Macroelements
Fully Nonlinear
Minimal Set
Triangulation

Keywords

  • Bernstein-Bézier techniques
  • fully nonlinear PDE
  • Monge-Ampère equation
  • multivariate splines

Cite this

Davydov, O., & Saeed, A. (2012). Stable splitting of bivariate spline spaces by Bernstein-Bézier methods. In J. D. Boissonnat et al (Ed.), Curves and Surfaces: Lecture Notes in Computer Science (Vol. 6920, pp. 220-235). (Lecture Notes in Computer Science). Springer-Verlag. https://doi.org/10.1007/978-3-642-27413-8_14
Davydov, Oleg ; Saeed, Abid. / Stable splitting of bivariate spline spaces by Bernstein-Bézier methods. Curves and Surfaces: Lecture Notes in Computer Science. editor / J.D. Boissonnat et al . Vol. 6920 Springer-Verlag, 2012. pp. 220-235 (Lecture Notes in Computer Science).
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Davydov, O & Saeed, A 2012, Stable splitting of bivariate spline spaces by Bernstein-Bézier methods. in JD Boissonnat et al (ed.), Curves and Surfaces: Lecture Notes in Computer Science. vol. 6920, Lecture Notes in Computer Science, Springer-Verlag, pp. 220-235, Curves and Surfaces - 7th International Conference, Avignon, France, 24/06/12. https://doi.org/10.1007/978-3-642-27413-8_14

Stable splitting of bivariate spline spaces by Bernstein-Bézier methods. / Davydov, Oleg; Saeed, Abid.

Curves and Surfaces: Lecture Notes in Computer Science. ed. / J.D. Boissonnat et al . Vol. 6920 Springer-Verlag, 2012. p. 220-235 (Lecture Notes in Computer Science).

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

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Davydov O, Saeed A. Stable splitting of bivariate spline spaces by Bernstein-Bézier methods. In Boissonnat et al JD, editor, Curves and Surfaces: Lecture Notes in Computer Science. Vol. 6920. Springer-Verlag. 2012. p. 220-235. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-642-27413-8_14