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A comparative Fourier analysis of discontinuous Galerkin schemes for advection–diffusion with respect to BR1, BR2, and local discontinuous Galerkin diffusion discretization
Author(s) -
Ortleb Sigrun
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6509
Subject(s) - discontinuous galerkin method , discretization , mathematics , advection , legendre polynomials , diffusion , galerkin method , flux (metallurgy) , convection–diffusion equation , mathematical analysis , finite element method , physics , materials science , metallurgy , thermodynamics
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.