International Conference on Multivariate Approximation
September 24-27, 2011

Ortho-projectors onto linear spline spaces over arbitrary triangulations: L-infinity-bounds

Peter Oswald
We will discuss the $L_\infty$ boundedness of the $L_2$-orthoprojection onto spaces of linear splines over arbitrary triangulations in two dimensions. Emphasis is on criteria guaranteeing uniform boundedness of the $L_\infty$ bounds, and (motivated by needs in the analysis of the finite element method) the case the triangulation is obtained from a rectangular tensor-product partition by further subdivision.