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 reproduction of second-degree polynomials, approximation order, conditions for convexity preservation. In particular, σ quasi-uniform grids with σ≤4, get quasi C3 that maintains properties initial data. give some numerical experiments regarding order