A nonlinear interpolatory reconstruction operator on non uniform grids

TL;DR

This paper introduces a nonlinear interpolation operator called PPH for non-uniform grids, analyzing its properties like polynomial reproduction, approximation accuracy, and convexity preservation.

Contribution

The paper presents the definition and analysis of a new nonlinear reconstruction operator PPH tailored for non-uniform grids, highlighting its key properties.

Findings

Reproduces second-degree polynomials.

Achieves specific approximation order.

Conditions for convexity preservation established.

Abstract

This paper is devoted to introduce the non linear reconstruction operator PPH on non uniform grids. We define this operator and we study its main properties such as reproduction of polynomials of second degree, approximation order and conditions for convexity preservation.