On Quasi-Interpolation Operators in Spline Spaces

Abstract

We propose the construction of a class of L2 stable quasi-interpolationoperators onto the space of splines on tensor-product meshes, in any space dimension. The estimate we propose is robust with respect to knot repetition and to knot ?vicinity? (up to p+1 knots), so it applies to the most general scenario in which the B-spline functions are known to be well defined.