# High order entropy preserving ADER scheme

Published in arXiv preprint, 2022

Recommended citation: E. Gaburro, P. Öffner, M. Ricchiuto and D. Torlo. (2022). "High order entropy preserving ADER scheme. " arXiv preprint, 2022. https://arxiv.org/abs/2206.03889. https://arxiv.org/abs/2206.03889

This is a work in collaboration with Elena Gaburro, Philipp Öffner and Mario Ricchiuto.

In this paper, we develop a fully discrete entropy preserving ADER-Discontinuous Galerkin (ADER-DG) method. To obtain this desired result, we equip the space part of the method with entropy correction terms that balance the entropy production in space, inspired by the work of Abgrall. Whereas for the time-discretization we apply the relaxation approach introduced by Ketcheson that allows to modify the timestep to preserve the entropy to machine precision. Up to our knowledge, it is the first time that a provable fully discrete entropy preserving ADER-DG scheme is constructed. We verify our theoretical results with various numerical simulations.