In the present work, we propose to extend to the Stokes problem a fictitiousdomain approach inspired by eXtended Finite Element Method and studied forPoisson problem in [Renard]. The method allows computations in domains whoseboundaries 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-setfunction. Dirichlet boundary conditions are taken into account using Lagrangemultiplier. A stabilization term is introduced to improve the approximation ofthe normal trace of the Cauchy stress tensor at the interface and avoid theinf-sup condition between the spaces for velocity and the Lagrange multiplier.Convergence analysis is given and several numerical tests are performed toillustrate the capabilities of the method.
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