Abstract

In this work, we extend the equal-order stabilized scheme discussed in [Franca et al., Comput. Methods Appl. Mech. Engrg. 99 (1992) 209-233] to incorporate slip (i.e., Navier) boundary conditions for the stationary Navier-Stokes equations. We present a robust formulation for the implementation of slip boundary conditions using Nitsche's method on arbitrarily complex boundaries. Under mild assumptions, we establish the well-posedness of the discrete problem along with optimal convergence rates for the approximation error. Furthermore, we prove the efficiency and reliability of residual-based aposteriori error estimators for the stationary discrete problem. Several standard numerical tests are provided to validate the theoretical results. The proposed method integrates naturally within the finite element framework, offering both high accuracy and enhanced flexibility in the choice of finite element pairs.