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) |
|---|---|
| Pages (from-to) | 327-347 |
| Number of pages | 21 |
| Journal | Advances in Computational Mathematics |
| Volume | 39 |
| Issue number | 2 |
| DOIs | |
| State | Published - Aug 2013 |
| Externally published | Yes |
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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 journal › Article
}
TY - JOUR
T1 - Interpolation error estimates for mean value coordinates over convex polygons
AU - Rand, Alexander
AU - Gillette, Andrew
AU - Bajaj, Chandrajit
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 -