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.

中文翻译：

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凸多边形上平均值坐标的插值误差估计。

与 Gillette 等人对 Harmonic、Wachspress 和 Sibson 坐标显示的估计值类似。（Adv Comput Math 37(3), 417–439​​, 2012），我们证明了适用于标准有限元分析的凸多边形平均值坐标的插值误差估计。我们的分析基于为所有直径满足某些简单几何限制的凸多边形的平均值函数的梯度提供统一的界限。这项工作严格地观察到平均值坐标的实际优势：与 Wachspress 坐标不同，平均值坐标的梯度不会随着多边形的内角接近π而变大。