In this paper, we formulate, analyse and implement the discrete formulation of the Brinkman problem with mixed boundary conditions, including slip boundary condition, using the Nitsche's technique for virtual element methods. The divergence conforming virtual element spaces for the velocity function and piecewise polynomials for pressure are approached for the discrete scheme. We derive a robust stability analysis of the Nitsche stabilized discrete scheme for this model problem. We establish an optimal and vigorous a priori error estimates of the discrete scheme with constants independent of the viscosity. Moreover, a set of numerical tests demonstrates the robustness with respect to the physical parameters and verifies the derived convergence results.

翻译：本文针对含滑移边界条件的混合边界Brinkman问题，采用Nitsche技术构建了虚拟元方法的离散格式，并进行了理论分析与数值实现。离散方案采用速度函数的散度相容虚拟元空间与压力的分片多项式空间。针对该模型问题，我们推导了Nitsche稳定化离散格式的鲁棒稳定性分析，建立了与黏度系数无关的常数最优强先验误差估计。此外，通过系列数值实验验证了方法对物理参数的鲁棒性，并证实了所推导的收敛性结果。