In this paper, we present a conforming discontinuous Galerkin (CDG) finite element method for Brinkman equations. The velocity stabilizer is removed by employing the higher degree polynomials to compute the weak gradient. The theoretical analysis shows that the CDG method is actually stable and accurate for the Brinkman equations. Optimal order error estimates are established in $H^1$ and $L^2$ norm. Finally, numerical experiments verify the stability and accuracy of the CDG numerical scheme.

翻译：本文提出了一种适用于Brinkman方程的协调间断Galerkin（CDG）有限元方法。通过采用高次多项式计算弱梯度，消除了速度稳定项。理论分析表明，CDG方法对于Brinkman方程具有稳定的收敛性和精确性。我们建立了$H^1$和$L^2$范数下的最优阶误差估计。最后，数值实验验证了CDG数值格式的稳定性和精度。