Aufsatz
A comparative Fourier analysis of discontinuous Galerkin schemes for advection–diffusion with respect to BR1, BR2, and local discontinuous Galerkin diffusion discretization
Zusammenfassung
This work compares the wave propagation properties of discontinuous Galerkin (DG) schemes for advection–diffusion problems with respect to the behavior of classical discretizations of the diffusion terms, that is, two versions of the local discontinuous Galerkin (LDG) scheme as well as the BR1 and the BR2 scheme. The analysis highlights a significant difference between the two possible ways to choose the alternating LDG fluxes showing that the variant that is inconsistent with the upwind advective flux is more accurate in case of advection–diffusion discretizations. Furthermore, whereas for the BR1 scheme used within a third order DG scheme on Gauss‐Legendre nodes, a higher accuracy for well‐resolved problems has previously been observed in the literature, this work shows that higher accuracy of the BR1 discretization only holds for odd orders of the DG scheme. In addition, this higher accuracy is generally lost on Gauss–Legendre–Lobatto nodes.
Zitierform
In: Mathematical Methods in the Applied Sciences Volume 43 / Issue 13 (2020-05-14) , S. 7841-7863 ; EISSN 1099-1476Förderhinweis
Gefördert im Rahmen des Projekts DEALZitieren
@article{doi:10.17170/kobra-202007241488,
author={Ortleb, Sigrun},
title={A comparative Fourier analysis of discontinuous Galerkin schemes for advection–diffusion with respect to BR1, BR2, and local discontinuous Galerkin diffusion discretization},
journal={Mathematical Methods in the Applied Sciences},
year={2020}
}
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2020-07-27T09:44:53Z 2020-07-27T09:44:53Z 2020-05-14 doi:10.17170/kobra-202007241488 http://hdl.handle.net/123456789/11657 Gefördert im Rahmen des Projekts DEAL eng Namensnennung 4.0 International http://creativecommons.org/licenses/by/4.0/ advection-diffusion problems diffusion fluxes discontinuous Galerkin methods dispersion relations Fourier analysis 510 A comparative Fourier analysis of discontinuous Galerkin schemes for advection–diffusion with respect to BR1, BR2, and local discontinuous Galerkin diffusion discretization Aufsatz This work compares the wave propagation properties of discontinuous Galerkin (DG) schemes for advection–diffusion problems with respect to the behavior of classical discretizations of the diffusion terms, that is, two versions of the local discontinuous Galerkin (LDG) scheme as well as the BR1 and the BR2 scheme. The analysis highlights a significant difference between the two possible ways to choose the alternating LDG fluxes showing that the variant that is inconsistent with the upwind advective flux is more accurate in case of advection–diffusion discretizations. Furthermore, whereas for the BR1 scheme used within a third order DG scheme on Gauss‐Legendre nodes, a higher accuracy for well‐resolved problems has previously been observed in the literature, this work shows that higher accuracy of the BR1 discretization only holds for odd orders of the DG scheme. In addition, this higher accuracy is generally lost on Gauss–Legendre–Lobatto nodes. open access Ortleb, Sigrun doi:10.1002/mma.6509 Gleichung Fourier-Analyse Galerkin-Methode Dispersionsrelation publishedVersion EISSN 1099-1476 Issue 13 Mathematical Methods in the Applied Sciences 7841-7863 Volume 43 false
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