Approximate Hermite quasi-interpolation

Abstract

In this article, 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.

Keywords:

• Hermite quasi-interpolation
• multivariate approximation
• error estimates
• harmonic functions

AMS Subject Classifications: :

• 41A30
• 65D15
• 41A63
• 41A25