Error estimates for generalized barycentric interpolation

Andrew Gillette, Alexander Rand, Chandrajit Bajaj

Research output: Contribution to journalArticle

47 Scopus citations

Abstract

We prove the optimal convergence estimate for first-order interpolants used in finite element methods based on three major approaches for generalizing barycentric interpolation functions to convex planar polygonal domains. The Wachspress approach explicitly constructs rational functions, the Sibson approach uses Voronoi diagrams on the vertices of the polygon to define the functions, and the Harmonic approach defines the functions as the solution of a PDE. We show that given certain conditions on the geometry of the polygon, each of these constructions can obtain the optimal convergence estimate. In particular, we show that the well-known maximum interior angle condition required for interpolants over triangles is still required for Wachspress functions but not for Sibson functions.

Original languageEnglish (US)
Pages (from-to)417-439
Number of pages23
JournalAdvances in Computational Mathematics
Volume37
Issue number3
DOIs
StatePublished - Sep 1 2012
Externally publishedYes

Keywords

  • Barycentric coordinates
  • Finite element method
  • Interpolation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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