$hp$-optimal convergence of the original DG method for linear hyperbolic problems on special simplicial meshes - École des Ponts ParisTech Access content directly
Preprints, Working Papers, ... Year : 2024

$hp$-optimal convergence of the original DG method for linear hyperbolic problems on special simplicial meshes

Abstract

We prove hp-optimal error estimates for the original DG method when approximating solutions to first-order hyperbolic problems with constant convection fields in the $L^2$ and DG norms. The main theoretical tools used in the analysis are novel $hp$-optimal approximation properties of the special projector introduced in [Cockburn, Dong, Guzman, SINUM, 2008]. We assess the numerical results on some test cases.
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Dates and versions

hal-04252310 , version 1 (20-10-2023)
hal-04252310 , version 2 (08-11-2023)
hal-04252310 , version 3 (09-07-2024)

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  • HAL Id : hal-04252310 , version 3

Cite

Zhaonan Dong, Lorenzo Mascotto. $hp$-optimal convergence of the original DG method for linear hyperbolic problems on special simplicial meshes. 2024. ⟨hal-04252310v3⟩

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