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

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  • Lukáčová-Medvid’ová, Mária
  • Öffner, Philipp

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.

Suggested Citation

  • Lukáčová-Medvid’ová, Mária & Öffner, Philipp, 2023. "Convergence of discontinuous Galerkin schemes for the Euler equations via dissipative weak solutions," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    • Handle: RePEc:eee:apmaco:v:436:y:2023:i:c:s0096300322005823
    DOI: 10.1016/j.amc.2022.127508
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