We propose a hybridizable discontinuous Galerkin (HDG) method for Stokes equation based on strong symmetric stress formulations. Stress-based method stands out compared to gradient or vorticity-based methods by its simple and natural way of enforcing Neumann type boundary conditions. Our method uses the polynomial spaces of orders \({\text {k}}-({\text {k}}+1)-{\text {k}}\) for the stress–velocity–pressure triplet, and orders \({\text {k}}-({\text {k}}+1)\) for the tangential and the normal components of the numerical trace space. By sending the normal stabilization to infinity, we obtain another method that provides exactly divergence-free solution and is pressure-robust. We prove that both methods are optimal for all variables and achieve super-convergence for the numerical trace. In addition, we build a quantitative connection between the normal stabilization and the pressure-robustness. Numerical experiments are also presented to validate our theoretical discoveries.

我们提出了基于强对称应力公式的Stokes方程的可杂交不连续Galerkin（HDG）方法。与基于梯度或基于涡度的方法相比，基于应力的方法通过其简单自然的方式来执行诺伊曼型边界条件，从而脱颖而出。我们的方法将阶数\（{\ text {k}}-（{\ text {k}} + 1）-{\ text {k}} \）的多项式空间用于应力-速度-压力三元组，并且阶数\（{\ text {k}}-（{\ text {k}} + 1）\）用于数字迹线空间的切线和法线分量。通过将法线稳定化到无穷大，我们获得了另一种方法，该方法提供了完全无散度的解决方案，并且具有耐压性。我们证明这两种方法对于所有变量都是最优的，并且对于数值迹线实现了超收敛。此外，我们在正常稳定度和耐压性之间建立了定量的联系。还提出了数值实验，以验证我们的理论发现。