Approximating surface areas by interpolations on triangulations
Approximating surface areas by interpolations on triangulations
复制标题
通过三角测量插值近似表面积
DOI：
10.1007/s13160-017-0253-0
复制
发表时间：
2017
影响因子：
0.9
通讯作者：
Takuya TSUCHIYA
中科院分区：
文献类型：
--
作者：
Kenta KOBAYASHI;Takuya TSUCHIYA
我们考虑表面面积近似的拉格朗日和Crouzeix-Raviart插值三角剖分。对于拉格朗日插值，我们给出了Young关于三角剖分上内接多边形曲面的面积在最大角条件下收敛于原曲面面积的经典结果的另一种证明.对于Crouzeix-Raviart插值，我们证明了近似的表面面积收敛到原始表面的面积，而不需要三角剖分上的任何几何条件。
We consider surface area approximations by Lagrange and Crouzeix-Raviart interpolations on triangulations. For Lagrange interpolation, we give an alternative proof for Young’s classical result that claims the areas of inscribed polygonal surfaces converge to the area of the original surface under the maximum angle condition on the triangulation. For Crouzeix–Raviart interpolation we show that the approximated surface areas converge to the area of the original surface without any geometric conditions on the triangulation.