Nitsche stabilized virtual element approximations for a Brinkman problem with mixed boundary conditions

In this paper, we formulate, analyze, 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. We propose a discretization by means of the virtual elements presented in Beirão da Veiga et al. [ESAIM Math. Model. Numer. Anal. 51 (2017) 509–535]. We derive a robust stability analysis of the Nitsche stabilized discrete scheme for this model problem. We establish optimal 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.