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Fourier Analysis of DG Schemes for Advection‐Diffusion

Ortleb, Sigrun

This work compares the wave propagation properties of discontinuous Galerkin (DG) schemes for advection‐diffusion problems in particular with respect to the discretization of diffusion terms. Extending previous investigations, the advection discretization now additionally varies between the choices of central or upwind fluxes. The results show that a previously recognized better performance of central schemes for well‐resolved problems only hold for even polynomial degrees and that upwind‐type discretizations also perform better on Gauss‐Lobatto nodes.

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Citation
In: Proceedings in applied mathematics and mechanics (PAMM) Volume 20 / Issue 1 (2021-01-25) , S. ; EISSN 1617-7061
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@article{doi:10.17170/kobra-202101283078,
  author    ={Ortleb, Sigrun},
  title    ={Fourier Analysis of DG Schemes for Advection‐Diffusion},
  keywords ={510 and Harmonische Analyse and Diskontinuierliche Galerkin-Methode and Wellenausbreitung},
  copyright  ={http://creativecommons.org/licenses/by/4.0/},
  language ={en},
  journal  ={Proceedings in applied mathematics and mechanics (PAMM)},
  year   ={2021-01-25}
}