Discretization of the Navier-Stokes equations with slip boundary condition

We propose and analyze a two-level method of discretizing the nonlinear Nav ier-Stokes equations with slip boundary condition. The slip boundary condit ion is appropriate for problems that involve free boundaries, flows past ch emically reacting walls, and other examples where the usual no-slip conditi on 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 soluti on to solve a larger linear system on the fine mesh. The two-level method e xploits the quadratic nonlinearity in the Navier-Stokes equations. Our erro r 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. (C) 2001 John Wiley & Sons. Inc.