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 language | English (US) |
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Pages (from-to) | 327-347 |
Number of pages | 21 |
Journal | Advances in Computational Mathematics |
Volume | 39 |
Issue number | 2 |
DOIs | |
State | Published - Aug 1 2013 |
Externally published | Yes |
Keywords
- Barycentric coordinates
- Finite element method
- Interpolation
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics