A flux-differencing formulation with Gauss nodes

TL;DR

This paper introduces a flux-differencing formulation with Gauss nodes for DGSEM, enabling entropy-stable stabilization methods and extending accuracy improvements from Gauss-Lobatto to Gauss nodes.

Contribution

It extends telescopic derivative operators for DGSEM with Gauss nodes and proves their equivalence to matrix formulations, facilitating advanced stabilization techniques.

Findings

Formulation is equivalent to the matrix counterpart.

Enables entropy stability with Gauss nodes.

Extends stabilization methods to Gauss nodes.

Abstract

In this work, we propose an extension of telescopic derivative operators for the DGSEM with Gauss nodes, and we prove that this formulation is equivalent to its usual matrix counterpart. Among other possible applications, this allows extending the stabilization methods already developed for Gauss-Lobatto nodes to Gauss nodes, also ensuring properties such as entropy stability while retaining their improved accuracy.