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- W1986751024 abstract "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 $P_V$ cannot be bounded uniformly with respect to the partition. This fact is folklore among specialists in finite element methods and approximation theory but seemingly has never been formally proved." @default.
- W1986751024 created "2016-06-24" @default.
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- W1986751024 date "2008-01-01" @default.
- W1986751024 modified "2023-10-12" @default.
- W1986751024 title "A counterexample concerning the $L_2$-projector onto linear spline spaces" @default.
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- W1986751024 doi "https://doi.org/10.1090/s0025-5718-07-02059-5" @default.
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