We consider a formulation for the Stokes problem in which the velocity is sought in H(curl). The tangential trace is well-defined in this space, but if we impose zero tangential velocity as an essential boundary condition, then the system is not guaranteed to be well-posed.
Instead, we propose to impose the no-slip condition weakly using Nitsche’s method. Using mesh-dependent norms, we show stability of the resulting discrete system and derive a priori error estimates. These estimates are improved in $L^2$ using duality techniques.
The optimal convergence of the velocity is shown both theoretically and numerically. The pressure, on the other hand, exhibits a half order convergence loss, in agreement with the theoretical estimates.
A closely related study concerning Navier-slip conditions can be found here.