On the convexity preservation of a quasi C3 nonlinear interpolatory reconstruction operator on σ quasi-uniform grids

This paper is devoted to introducing a nonlinear reconstruction operator, the piecewise polynomial harmonic (PPH), on nonuniform grids. We define this operator and we study its main properties, such as its reproduction of second-degree polynomials, approximation order, and conditions for convexity preservation. In particular, for σ quasi-uniform grids with σ≤4, we get a quasi C3 reconstruction that maintains the convexity properties of the initial data. We give some numerical experiments regarding the approximation order and the convexity preservation.This research was funded by the FUNDACIÓN SÉNECA, AGENCIA DE CIENCIA Y TECNOLOGÍA DE LA REGIÓN DE MURCIA grant number 20928/PI/18, and by the Spanish national research project PID2019-108336GB-I00