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Advances in Computational Mathematics

, Volume 39, Issue 2, pp 327–347 | Cite as

Interpolation error estimates for mean value coordinates over convex polygons

  • Alexander Rand
  • Andrew Gillette
  • Chandrajit BajajEmail author
Article

Abstract

In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in Gillette et al. (Adv Comput Math 37(3), 417–439, 2012), we prove interpolation error estimates for the mean value coordinates on convex polygons suitable for standard finite element analysis. Our analysis is based on providing a uniform bound on the gradient of the mean value functions for all convex polygons of diameter one satisfying certain simple geometric restrictions. This work makes rigorous an observed practical advantage of the mean value coordinates: unlike Wachspress coordinates, the gradients of the mean value coordinates do not become large as interior angles of the polygon approach π.

Keywords

Barycentric coordinates Interpolation Finite element method 

Mathematics Subject Classifications (2010)

65D05 65N15 65N30 

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Alexander Rand
    • 1
  • Andrew Gillette
    • 2
  • Chandrajit Bajaj
    • 3
    Email author
  1. 1.CD-adapcoAustinUSA
  2. 2.Department of MathematicsUniversity of California, San DiegoSan DiegoUSA
  3. 3.Department of Computer Science, Institute for Computational Engineering and SciencesUniversity of Texas at AustinAustinUSA

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