I would like to set a slip boundary condition u\cdot n = 0 for my Stokes problem (as e.g. described here). It is very easy for boundaries parallel to the coordinate axis. But how can I define that boundary condition for arbitrarily shaped surfaces where n is different everywhere and not parallel to the axes?
that’s a good argument for switching to H(div)-conforming methods
Alternatively, you can also use Nitsche’s methods for u \cdot n=0 for H^1-conforming velocities.
A simple method is adding \int_\Gamma 10^{10} u_n v_n ds, but think twice about the integration rule on curved boundaries.