On the Convexity Preservation of a Quasi C 3 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 C 3 reconstruction that maintains the convexity properties of the initial data. We give some numerical experiments regarding the approximation order and the convexity preservation. [ABSTRACT FROM AUTHOR]