Nitsche method for Navier–Stokes equations with slip boundary conditions: convergence analysis and VMS-LES stabilization

In this paper, we analyze Nitsche’s method for the stationary Navier–Stokes equations on Lipschitz domains under minimal regularity assumptions. Our analysis provides a robust formulation for implementing slip (i.e., Navier) boundary conditions in arbitrarily complex boundaries. The well-posedness of the discrete problem is established using the Banach Nečas–Babuška and Banach fixed point theorems under standard small data assumptions. We also provide optimal convergence rates for the approximation error. Furthermore, we propose a quasi-static VMS-LES formulation with Nitsche for the Navier–Stokes equations with slip boundary conditions to address the simulation of incompressible fluids at high Reynolds numbers. We validate our theory through several numerical tests in well-established benchmark problems.