  In this note we design a cut finite element method for a low order divergence
free element applied to a boundary value problem subject to Stokes' equations.
For the imposition of Dirichlet boundary conditions we consider either
Nitsche's method or a stabilized Lagrange multiplier method. In both cases the
normal component of the velocity is constrained using a multiplier, different
from the standard pressure approximation. The divergence of the approximate
velocities is pointwise zero over the whole mesh domain, and we derive optimal
error estimates for the velocity and pressures, where the error constant is
independent of how the physical domain intersects the computational mesh, and
of the regularity of the pressure multiplier imposing the divergence free
condition.

Numerical Analysis;Numerical Analysis