Interpolation error estimates for mean value coordinates over convex polygons

Alexander Rand, Andrew Gillette, Chandrajit Bajaj

Research output: Contribution to journalArticle

25 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)327-347
Number of pages21
JournalAdvances in Computational Mathematics
Volume39
Issue number2
DOIs
StatePublished - Aug 2013
Externally publishedYes

Fingerprint

Interpolation Error
Convex polygon
Mean Value
Error Estimates
Interpolation
Finite element method
Interior angle
Gradient
Uniform Bound
Value Function
Polygon
Harmonic
Finite Element
Restriction
Estimate

Keywords

  • Barycentric coordinates
  • Finite element method
  • Interpolation

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

Cite this

Interpolation error estimates for mean value coordinates over convex polygons. / Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit.

In: Advances in Computational Mathematics, Vol. 39, No. 2, 08.2013, p. 327-347.

Research output: Contribution to journalArticle

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