A counterexample concerning the $L_2$-projector onto linear spline spaces
A counterexample concerning the $L_2$-projector onto linear spline spaces
For the $L_2$-orthogonal projection $P_V$ onto spaces of linear splines over simplicial partitions in polyhedral domains in $\mathbb {R}^d$, $d>1$, we show that in contrast to the one-dimensional case, where $\|P_V\|_{L_\infty \to L_\infty } \le 3$ independently of the nature of the partition, in higher dimensions the $L_\infty$-norm of $P_V$ …