On quasi-interpolation operators in spline spaces

Abstract

We propose the construction of a class of L2 stable quasi-interpolation operators 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.