A counterexample concerning the L_2-projector onto linear spline spaces
数值分析
2008-08-05 v1
摘要
For the L_2-orthogonal projector P onto spaces of linear splines over simplicial partitions of polyhedral domains in R^d, d>1, we show that the L_infty norm of P cannot be bounded uniformly with respect to the partition. This is in contrast to d=1, where these norms are bounded by 3 independently of the partition. This negative result is folklore among specialists in finite element methods and approximation theory but seemingly has never been formally proved.
引用
@article{arxiv.math/0611573,
title = {A counterexample concerning the L_2-projector onto linear spline spaces},
author = {Peter Oswald},
journal= {arXiv preprint arXiv:math/0611573},
year = {2008}
}
备注
7 pages, 1 figure, submitted to Mathematics of Computation