High order entropy preserving ADER-DG schemes

Elena Gaburro, Philipp Öffner, Mario Ricchiuto and Davide Torlo

Applied Mathematics and Computation, 2023, vol. 440, issue C

Abstract: 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.

Keywords: Hyperbolic conservation laws; ADER; Discontinuous Galerkin; Entropy conservation/stability; Structure preserving; Relaxation method (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:440:y:2023:i:c:s0096300322007160

DOI: 10.1016/j.amc.2022.127644

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