We present a new stabilized finite element method for Navier-Stokes equations with friction slip boundary conditions based on Brezzi-Pitkäranta stabilized method. The stability and error estimates of numerical solutions in some norms are derived for standard one-level method. Combining the techniques of two-level discretization method, we propose two-level Newton iteration method and show the stability and error estimate. Finally, the numerical experiments are given to support the theoretical results and to check the efficiency of this two-level iteration method.
"Two-Level Brezzi-Pitkäranta Discretization Method Based on Newton Iteration for Navier-Stokes Equations with Friction Boundary Conditions." Abstr. Appl. Anal. 2014 1 - 14, 2014. https://doi.org/10.1155/2014/474160