On the suboptimality of the p-version discontinuous Galerkin methods for first order hyperbolic problems - Archive ouverte HAL Access content directly
Conference Papers Year :

On the suboptimality of the p-version discontinuous Galerkin methods for first order hyperbolic problems

(1, 2) , (3)
1
2
3

Abstract

We address the issue of the suboptimality in the p-version discontinuous Galerkin (dG) methods for first order hyperbolic problems. The convergence rate is derived for the upwind dG scheme on tensor product meshes in any dimension. The standard proof in seminal work [14] leads to suboptimal convergence in terms of the polynomial degree by 3/2 order for general convection fields, with the exception of piecewise multi-linear convection fields, which rather yield optimal convergence. Such suboptimality is not observed numerically. Thus, it might be caused by a limitation of the analysis, which we partially overcome: for a special class of convection fields, we shall show that the dG method has a p-convergence rate suboptimal by 1/2 order only.
Fichier principal
Vignette du fichier
WCCM&ECCOMMAS.pdf (293.32 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03104757 , version 1 (09-01-2021)

Identifiers

  • HAL Id : hal-03104757 , version 1

Cite

Zhaonan Dong, Lorenzo Mascotto. On the suboptimality of the p-version discontinuous Galerkin methods for first order hyperbolic problems. 14th WCCM-ECCOMAS Congress 2020, Jan 2021, Paris, France. ⟨hal-03104757⟩
64 View
110 Download

Share

Gmail Facebook Twitter LinkedIn More