A priori error analysis for Navier Stokes equations with slip boundary conditions of friction type

Abstract

The time dependent Navier Stokes equations under nonlinear slip boundary conditions are discretized by backward Euler scheme in time and finite elements in space. We derive error estimates for the semi-discrete problems. The focus on the semi discrete problem in time is to obtain convergence rate without extra regularity on the weak solution by following Nochetto et al. (Commun Pure Appl Math 53(5):525–589, 2000). The semi discrete problem in space is analyzed with the help of the Stokes operator introduced. Finally we use the triangle inequality to derive the global a priori error estimates.