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Mathematics > Numerical Analysis

arXiv:2206.03889 (math)
[Submitted on 8 Jun 2022]

Title:High order entropy preserving ADER scheme

Authors:Elena Gaburro, Philipp Öffner, Mario Ricchiuto, Davide Torlo
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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.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2206.03889 [math.NA]
  (or arXiv:2206.03889v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2206.03889
Related DOI: https://doi.org/10.1016/j.amc.2022.127644

Submission history

From: Davide Torlo [view email]
[v1] Wed, 8 Jun 2022 13:40:51 UTC (8,920 KB)
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