Two-Level Brezzi-Pitkäranta Discretization Method Based on Newton Iteration for Navier-Stokes Equations with Friction Boundary Conditions

Abstract EN

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.