In this paper we derive approximate quasi-interpolants when the values of a function u and of some of its derivatives are prescribed at the points of a uniform grid. As a byproduct of these formulas we obtain very simple approximants which provide high order approximations for solutions to elliptic differential equations with constant coefficients.
@article{arxiv.0806.2546,
title = {Approximate Hermite quasi-interpolation},
author = {Flavia Lanzara and Vladimir Maz'ya and Gunther Schmidt},
journal= {arXiv preprint arXiv:0806.2546},
year = {2008}
}