Stokes and Navier-Stokes equations under power law slip boundary condition: Numerical analysis

In this work, we study theoretically and numerically the equations of Stokes Navier-Stokes under power law slip boundary condition. We establish existence a unique solution by using monotone operators theory for whereas equations, construct means Galerkin's approximation combined with some compactness results. Next, formulate analyze finite element approximations associated to these problems. derive optimal sub-optimal priori error estimate both problems depending how monotonicity is used. Iterative schemes solving nonlinear are formulated convergence studied. Numerical experiments presented confirm theoretical findings.