title: Interpolation Error Estimates for Mean Value Coordinates over Convex Polygons.
abstract: In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in [Gillette et al., AiCM, to appear], 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 gradient of the mean value coordinates does not become large as interior angles of the polygon approach π.
authors.affiliation: Institute for Computational Engineering and Sciences, University of Texas at Austin, arand@ices.utexas.edu.
authors.forename: Alexander
authors.initials: A
authors.lastname: Rand
authors.forename: Andrew
authors.initials: A
authors.lastname: Gillette
authors.forename: Chandrajit
authors.initials: C
authors.lastname: Bajaj
keywords: Barycentric coordinates; finite element method; interpolation
references.citation: Adv Comput Math. 2012 Oct 1;37(3):417-439
references.pmid: 23338826
references.citation: IEEE Comput Graph Appl. 2012 Jul-Aug;32(4):68-78
references.pmid: 24806634