In [SIAM J. Numer. Anal., 59 (2), 720-745], we proved quasi-optimal $L^\infty$ estimates (up to logarithmic factors) for the solution of Poisson's equation by a hybridizable discontinuous Galerkin (HDG) method. However, the estimates only work in 2D. In this paper, we obtain sharp (without logarithmic factors) $L^\infty$ estimates for the HDG method in both 2D and 3D. Numerical experiments are presented to confirm our theoretical result.

翻译：在[SIAM J. Numer. Anal., 59(2), 720-745]中,我们证明,用一种混合的不连续加热金(HDG)方法解决Poisson的等式的估算值(最高为对数系数)几乎是理想的美元。然而,只有2D的估算值。 在本文件中,我们获得了2D和3D中HD方法的精确(无对数系数)的估算值。 数字实验证实了我们的理论结果。