Weak imposition of “no-slip” conditions in finite element methods

We begin the analysis of two schemes for imposing weakly the “no-slip” boundary conditions in the Navier-Stokes equations. The first is via a Lagrange multiplier constraining no tangential velocity on the boundary and the second is via penalization of tangential velocities along boundaries. Our analysis in this first step is for the Stokes problem although the motivation for relaxing this essential boundary condition comes from higher Reynolds number flow.