  In the present work, we propose to extend to the Stokes problem a fictitious
domain approach inspired by eXtended Finite Element Method and studied for
Poisson problem in [Renard]. The method allows computations in domains whose
boundaries do not match. A mixed finite element method is used for fluid flow.
The interface between the fluid and the structure is localized by a level-set
function. Dirichlet boundary conditions are taken into account using Lagrange
multiplier. A stabilization term is introduced to improve the approximation of
the normal trace of the Cauchy stress tensor at the interface and avoid the
inf-sup condition between the spaces for velocity and the Lagrange multiplier.
Convergence analysis is given and several numerical tests are performed to
illustrate the capabilities of the method.
