This paper develops a class of robust weak Galerkin methods for the stationary incompressible convective Brinkman-Forchheimer equations. The methods adopt piecewise polynomials of degrees $m\ (m\geq1)$ and $m-1$ respectively for the approximations of velocity and pressure variables inside the elements and piecewise polynomials of degrees $k \ ( k=m-1,m)$ and $m$ respectively for their numerical traces on the interfaces of elements, and are shown to yield globally divergence-free velocity approximation. Existence and uniqueness results for the discrete schemes, as well as optimal a priori error estimates, are established. A convergent linearized iterative algorithm is also presented. Numerical experiments are provided to verify the performance of the proposed methods

翻译：本文针对稳态不可压缩对流Brinkman-Forchheimer方程，发展了一类鲁棒弱Galerkin方法。该方法在单元内部采用次数分别为$m\ (m\geq1)$和$m-1$的分片多项式逼近速度和压力变量，在单元界面上分别采用次数为$k \ (k=m-1,m)$和$m$的分片多项式逼近速度和压力的数值迹，并证明可得到全局无散度的速度逼近。建立了离散格式的存在唯一性结果以及最优先验误差估计，同时给出了收敛的线性化迭代算法。最后通过数值实验验证了所提方法的性能。