  We propose a Nitsche-based fictitious domain method for the three field
Stokes problem in which the boundary of the domain is allowed to cross through
the elements of a fixed background mesh. The dependent variables of velocity,
pressure and extra-stress tensor are discretised on the background mesh using
linear finite elements. This equal order approximation is stabilized using a
continuous interior penalty (CIP) method. On the unfitted domain boundary,
Dirichlet boundary conditions are weakly enforced using Nitsche's method. We
add CIP-like ghost penalties in the boundary region and prove that our scheme
is inf-sup stable and that it has optimal convergence properties independent of
how the domain boundary intersects the mesh. Additionally, we demonstrate that
the condition number of the system matrix is bounded independently of the
boundary location. We corroborate our theoretical findings with numerical
examples.
