This paper proposes semi-discrete and fully discrete hybridizable discontinuous Galerkin (HDG) methods for the Burgers' equation in two and three dimensions. In the spatial discretization, we use piecewise polynomials of degrees $ k \ (k \geq 1), k-1$ and $ l \ (l=k-1; k) $ to approximate the scalar function, flux variable and the interface trace of scalar function, respectively. In the full discretization method, we apply a backward Euler scheme for the temporal discretization. Optimal a priori error estimates are derived. Numerical experiments are presented to support the theoretical results.

翻译：本文建议用半分解和完全离散的混合不连续加列金(HDG)方法,用于汉堡方程式的两个和三个维度。在空间离散化中,我们使用零碎的多元度(°k k\geq 1), k-1美元和 l \ (l=k-1; k) 美元,分别用于接近弧函数、通量变量和斜度函数的界面痕量。在完全离散法中,我们用落后的Euler 方法来计算时间离散。得出了最佳的先验误差估计值。提供了数字实验来支持理论结果。