Convergence of discontinuous Galerkin schemes for the Euler equations via dissipative weak solutions

Lukáčová-Medvid’ová, Mária and Philipp Öffner

Applied Mathematics and Computation, 2023, vol. 436, issue C

Abstract: In this paper, we present convergence analysis of high-order finite element based methods, in particular, we focus on a discontinuous Galerkin scheme using summation-by-parts operators. To this end, it is crucial that structure preserving properties, such as positivity preservation and entropy inequality hold. We demonstrate how to ensure them and prove the convergence of our multidimensional high-order DG scheme via dissipative weak solutions. In numerical simulations, we verify our theoretical results.

Keywords: Euler equations; Dissipative weak solutions; Convergence analysis; Discontinuous Galerkin; Structure preserving (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:436:y:2023:i:c:s0096300322005823

DOI: 10.1016/j.amc.2022.127508

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