Weak imposition of boundary conditions for the Navier-Stokes equations

We prove the convergence of a finite element method for the NavierStokes equations in which the no-slip condition, u ·τ i = 0 on Γ for i = 1, 2 is imposed by a penalty method and the no-penetration condition, u·n = 0 on Γ, is imposed by Lagrange multipliers. This approach has been studied for the Stokes problem in [2]. In most flows the Reynolds number is not This work partially supported by NSF grants DMS9972622, INT9814115, and INT9805563. [email protected], http://www.math.pitt.edu/∼atife