TY - JOUR

T1 - Interpolation error estimates for mean value coordinates over convex polygons

AU - Rand, Alexander

AU - Gillette, Andrew

AU - Bajaj, Chandrajit

N1 - Funding Information:
This research was supported in part by NIH contracts R01-EB00487, R01-GM074258, and a grant from the UT-Portugal CoLab project. This work was performed while the first author was at the Institute for Computational Engineering and Sciences at the University of Texas at Austin.

PY - 2013/8

Y1 - 2013/8

N2 - 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.

AB - 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.

KW - Barycentric coordinates

KW - Finite element method

KW - Interpolation

UR - http://www.scopus.com/inward/record.url?scp=84884921576&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884921576&partnerID=8YFLogxK

U2 - 10.1007/s10444-012-9282-z

DO - 10.1007/s10444-012-9282-z

M3 - Article

AN - SCOPUS:84884921576

VL - 39

SP - 327

EP - 347

JO - Advances in Computational Mathematics

JF - Advances in Computational Mathematics

SN - 1019-7168

IS - 2

ER -