A counterexample concerning the L_2-projector onto linear spline spaces

Details A counterexample concerning the L_2-projector onto linear spline spaces A counterexample concerning the L_2-projector onto linear spline spaces

2006-11-19

arxiv.org/abs/math/0611573v1

Mathematics of Computation, vol. 77, n. 261, Jan. 2008, 221-226.

Mathematics

Numerical Analysis

7 pages, 1 figure, submitted to Mathematics of Computation

Scientific paper

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.

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