A nonlinear PPH-type reconstruction based on equilateral triangles

TL;DR

This paper introduces a new nonlinear reconstruction operator for 2D triangular domains, leveraging harmonic mean properties, with proven approximation capabilities and numerical tests showing reduced Gibbs effects.

Contribution

It presents a novel nonlinear reconstruction operator based on equilateral triangles, with theoretical approximation results and numerical evidence of improved performance.

Findings

Proven approximation properties of the operator

Numerical tests show avoidance of Gibbs effects

Operator designed specifically for equilateral triangle meshes

Abstract

In this paper we introduce a new nonlinear reconstruction operator over two dimensional triangularized domains with equilateral triangles. We focus on the local definition of the operator. The ideas behind this definition come from some basic properties of the Harmonic mean of three positive values. We prove some results regarding the approximation properties of the operator and we carry out some numerical tests giving evidence of the avoidance of any Gibbs effects.