标题： 线性拉格朗日插值在最大范数下的误差常数估计 显示英文标题

标题： Error constant estimation under the maximum norm for linear Lagrange interpolation

摘要： 对于三角形区域上的拉格朗日插值，我们提出了一种高效的算法，通过有限元方法（FEM）严格评估最大范数下的插值误差常数。 在求解对应于插值误差常数的优化问题时，约束条件中的最大范数是处理起来最困难的部分。 为了解决这个困难，提出了一种新方法，结合了与 Fujino--Morley FEM 空间相关的插值正交性以及 FEM 空间中函数的伯恩斯坦表示的凸包性质。 给出了不同类型的三角形插值误差常数的下界和上界的数值结果，以验证所提方法的效率。 显示英文摘要

摘要： For the Lagrange interpolation over a triangular domain, we propose an efficient algorithm to rigorously evaluate the interpolation error constant under the maximum norm by using the finite element method (FEM). In solving the optimization problem corresponding to the interpolation error constant, the maximum norm in the constraint condition is the most difficult part to process. To handle this difficulty, a novel method is proposed by combining the orthogonality of the interpolation associated to the Fujino--Morley FEM space and the convex-hull property of the Bernstein representation of functions in the FEM space. Numerical results for the lower and upper bounds of the interpolation error constant for triangles of various types are presented to verify the efficiency of the proposed method.