Extending Babuska-Aziz's theorem to higher-order Lagrange interpolation
Extending Babuska-Aziz's theorem to higher-order Lagrange interpolation
复制标题
将 Babuska-Aziz 定理推广到高阶拉格朗日插值
DOI：
10.1007/s10492-016-0125-y
复制
发表时间：
2016
影响因子：
0.7
通讯作者：
T. Tsuchiya
中科院分区：
文献类型：
--
作者：
K. Kobayashi;T. Tsuchiya
We consider the error analysis of Lagrange interpolation on triangles and tetrahedrons. For Lagrange interpolation of order one, Babuška and Aziz showed that squeezing a right isosceles triangle perpendicularly does not deteriorate the optimal approximation order. We extend their technique and result to higher-order Lagrange interpolation on both triangles and tetrahedrons. To this end, we make use of difference quotients of functions with two or three variables. Then, the error estimates on squeezed triangles and tetrahedrons are proved by a method that is a straightforward extension of the original one given by Babuška-Aziz.
