Interpolation Error Estimates for Mean Value Coordinates over Convex Polygons
CD-adapco；Department of Mathematics, University of California, San Diego（加州大学圣地亚哥分校数学系）；Department of Computer Science, The University of Texas at Austin（德克萨斯大学奥斯汀分校计算机科学系）
与[Gillette et al., AiCM, doi:10.1007/s10444-011-9218-z]中针对调和、Wachspress和Sibson坐标的估计类似，我们证明了适用于标准有限元分析的凸多边形上均值坐标的插值误差估计。我们的分析基于为满足某些简单几何约束的单位直径凸多边形上的均值函数梯度提供一个统一界。这项工作严格证明了均值坐标的一个实际优势：与Wachspress坐标不同，当多边形内角接近π时，均值坐标的梯度不会变大。
英文摘要：
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 gradients of the mean value coordinates do not become large as interior angles of the polygon approach pi.
Stable High-Order Interpolation on the Grassmann Manifold by Maximum-Volume Coordinates and Arnoldi Orthogonalization
School of Mathematics and Physics, Xi’an Jiaotong-Liverpool University（西交利物浦大学数理学院）；Department of Mathematical Sciences, University of Liverpool（利物浦大学数学科学系）
A Wachspress-based transfinite formulation for exactly enforcing Dirichlet boundary conditions on convex polygonal domains in physics-informed neural networks
University of California（加州大学）；DS Simulia, Dassault Systèmes Inc.（达索系统公司）
