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.

Dong, Z., Mascotto, L. (2021). On the suboptimality of the p-version discontinuous galerkin methods for first order hyperbolic problems. In World Congress in Computational Mechanics and ECCOMAS Congress (pp.1-8). Scipedia S.L. [10.23967/wccm-eccomas.2020.033].

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

Mascotto, L.
2021

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.
Si
paper
Discontinuous Galerkin methods; Hp-finite element methods; Hyperbolic problems;
English
14th World Congress of Computational Mechanics and ECCOMAS Congress, WCCM-ECCOMAS 2020 - 11 January 2021 through 15 January 2021
Dong, Z., Mascotto, L. (2021). On the suboptimality of the p-version discontinuous galerkin methods for first order hyperbolic problems. In World Congress in Computational Mechanics and ECCOMAS Congress (pp.1-8). Scipedia S.L. [10.23967/wccm-eccomas.2020.033].
Dong, Z; Mascotto, L
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/337458
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