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 L2 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.

翻译：我们证明了原始DG方法在$L^2$和DG范数下逼近常对流场一阶双曲问题解时的$hp$最优误差估计。分析中采用的主要理论工具是[Cockburn, Dong, Guzman, SINUM, 2008]中引入的特殊投影算子的新型$hp$最优逼近性质。我们通过若干测试案例评估了数值结果。