Interpolation Error Estimates for Mean Value Coordinates

Details Interpolation Error Estimates for Mean Value Coordinates Interpolation Error Estimates for Mean Value Coordinates

2011-11-23

arxiv.org/abs/1111.5588v1

Mathematics

Numerical Analysis

18 pages

Scientific paper

In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in [Gillette et al., AiCM, doi:10.1007/s10444-011-9218-z], 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 pi.

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