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