This paper presents the interior penalty discontinuous Galerkin (IPDG) methods to solve the stationary Stokes equations with nonlinear damping term. The IPDG discrete schemes are established on general meshes. The corresponding consistency and stabilization of those schemes are proved. Subsequently, we analyze the existence, boundedness and uniqueness of the discrete solutions. Then the optimal error estimates are derived in the $L^2$-norm and $H^1$-like DG-norm for the velocity variable and $L^2$-norm for the pressure variable, respectively. Finally, some numerical experiments in two dimensional are reported to demonstrate the theoretical results and show the robustness of our discrete schemes.

本文提出了内部罚分不连续伽勒金（IPDG）方法来求解具有非线性阻尼项的平稳斯托克斯方程。IPDG离散方案是在通用网格上建立的。证明了这些方案的相应一致性和稳定性。随后，我们分析了离散解的存在性，有界性和唯一性。然后，在${\mathrm{大号}}^2$-规范和 $H^{\mathrm{1个}}$速度变量的类DG范数和 ${\mathrm{大号}}^2$-norm分别代表压力变量。最后，在二维上进行了一些数值实验，以证明理论结果并证明了离散方案的鲁棒性。