Pressure-robust Nitsche's method for Stokes problem with slip boundary conditions

This paper introduces a pressure-robust numerical scheme for the Stokes equations with slip boundary conditions, combining Nitsche's method with a divergence-free reconstruction operator. By introducing an auxiliary problem, we circumvent the incompatibility of the discrete saddle-point operator's properties (boundedness, coercivity, and inf-sup conditions) with the continuous function space and specific norm. This analysis identifies the mechanism underlying the pressure-dependent error propagation in classical formulations. To address this, we develop an enhanced discretization scheme by modifying the right-hand side volume term via a divergence-free reconstruction operator that maps test functions into the Raviart-Thomas finite element space, while keeping the right-hand side boundary terms unaltered. This modification ensure that the velocity estimate remains independent of both the viscosity coefficient and pressure magnitude.