Discretization of the Navier-Stokes equations with slip boundary condition

Abstract

We propose and analyze a two-level method of discretizing the nonlinear Navier-Stokes equations with slip boundary condition. The slip boundary condition is appropriate for problems that involve free boundaries, flows past chemically reacting walls, and other examples where the usual no-slip condition u = 0 is not valid. The two-level algorithm consists of solving a small nonlinear system of equations on the coarse mesh and then using that solution to solve a larger linear system on the fine mesh. The two-level method exploits the quadratic nonlinearity in the Navier-Stokes equations. Our error estimates show that it has optimal order accuracy, provided that the best approximation to the true solution in the velocity and pressure spaces is bounded above by the data. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 26–42, 2001