J. Alexandersen, N. Aage, C. S. Andreasen, and O. Sigmund, Topology optimisation for natural convection problems, International Journal for Numerical Methods in Fluids, vol.43, issue.5, pp.76-699, 2014.
DOI : 10.1002/fld.505

S. Amstutz, The topological asymptotic for the Navier-Stokes equations. ESAIM: Control, Optimisation and Calculus of Variations, pp.401-425, 2005.

S. Amstutz and A. Bonnafé, Topological derivatives for a class of quasilinear elliptic equations, Journal de Math??matiques Pures et Appliqu??es, vol.107, issue.4, 2016.
DOI : 10.1016/j.matpur.2015.11.015

C. S. Andreasen, A. R. Gersborg, and O. Sigmund, Topology optimization of microfluidic mixers, International Journal for Numerical Methods in Fluids, vol.106, issue.2, pp.61-498, 2009.
DOI : 10.1016/j.snb.2004.09.006

P. Angot, G. Carbou, and V. Péron, Asymptotic study for StokesBrinkman model with jump embedded transmission conditions, Asymptotic Analysis, vol.96, pp.3-4, 2016.
DOI : 10.3233/asy-151336
URL : https://hal.archives-ouvertes.fr/hal-01184429

F. Abergel and E. Casas, Some optimal control problems of multistate equations appearing in fluid mechanics. RAIRO-Modélisation mathématique et analyse numérique, pp.223-247, 1993.

C. Amrouche and N. E. Seloula, -THEORY FOR VECTOR POTENTIALS AND SOBOLEV'S INEQUALITIES FOR VECTOR FIELDS: APPLICATION TO THE STOKES EQUATIONS WITH PRESSURE BOUNDARY CONDITIONS, Mathematical Models and Methods in Applied Sciences, vol.1607, issue.01, pp.23-37, 2013.
DOI : 10.1007/BF02570870
URL : https://hal.archives-ouvertes.fr/hal-00868309

P. Angot, C. H. Bruneau, and P. Fabrie, A penalization method to take into account obstacles in incompressible viscous flows, Numerische Mathematik, vol.81, issue.4, pp.497-520, 1999.
DOI : 10.1007/s002110050401

J. M. Bernard, Non-standard Stokes and NavierStokes problems: existence and regularity in stationary case, Mathematical methods in the applied sciences, pp.25-627, 2002.
DOI : 10.1002/mma.260

C. Bernardi, T. Chacon-rebello, and D. Yakoubi, Finite Element Discretization of the Stokes and Navier--Stokes Equations with Boundary Conditions on the Pressure, SIAM Journal on Numerical Analysis, vol.53, issue.3
DOI : 10.1137/140972299
URL : https://hal.archives-ouvertes.fr/hal-00961653

C. Bernardi, C. Canuto, and Y. Maday, Spectral Approximations of the Stokes Equations with Boundary Conditions on the Pressure, SIAM Journal on Numerical Analysis, vol.28, issue.2, pp.333-362, 1991.
DOI : 10.1137/0728019

T. Borrvall and J. Petersson, Topology optimization of fluids in Stokes flow, International Journal for Numerical Methods in Fluids, vol.24, issue.1, pp.77-107, 2003.
DOI : 10.1007/978-3-662-12613-4

Y. Cao, M. Gunzburger, F. Hua, and X. Wang, Coupled Stokes-Darcy model with Beavers-Joseph interface boundary condition, Communications in Mathematical Sciences, vol.8, issue.1, pp.1-25, 2010.
DOI : 10.4310/CMS.2010.v8.n1.a2
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.145.2746

F. Cimolin and M. Discacciati, Navier???Stokes/Forchheimer models for filtration through porous media, Applied Numerical Mathematics, vol.72, pp.205-224, 2013.
DOI : 10.1016/j.apnum.2013.07.001

E. Casas, M. Mateos, and J. P. Raymond, Error Estimates for the Numerical Approximation of a Distributed Control Problem for the Steady-State Navier???Stokes Equations, SIAM Journal on Control and Optimization, vol.46, issue.3, pp.952-982, 2007.
DOI : 10.1137/060649999
URL : https://hal.archives-ouvertes.fr/hal-00635521

S. Court, M. Fournié, and A. Lozinski, A fictitious domain approach for the Stokes problem based on the extended finite element method, International Journal for Numerical Methods in Fluids, vol.35, issue.152, pp.73-99, 2014.
DOI : 10.2307/2006378

J. Cousteix and J. Mauss, Asymptotic analysis and boundary layers, 2007.

T. Dbouk, A review about the engineering design of optimal heat transfer systems using topology optimization, Applied Thermal Engineering, vol.112, pp.841-854, 2017.
DOI : 10.1016/j.applthermaleng.2016.10.134

M. Discacciati and A. Quarteroni, Navier-Stokes/darcy coupling: modeling, analysis, and numerical approximation, Revista Matem??tica Complutense, vol.22, issue.2, pp.315-426, 2009.
DOI : 10.5209/rev_REMA.2009.v22.n2.16263

M. Ehrhardt, An Introduction to Fluid-Porous Interface Coupling, 2010.
DOI : 10.2174/978160805254711201010003

A. Evgrafov, M. M. Gregersen, and M. P. Srensen, Convergence of Cell Based Finite Volume Discretizations for Problems of Control in the Conduction Coefficients, ESAIM: Mathematical Modelling and Numerical Analysis, vol.5, issue.6, pp.45-1059, 2011.
DOI : 10.1137/070699822

A. Evgrafov, The limits of porous materials in the topology optimization of Stokes flows Applied mathematics & optimization, pp.263-277, 2005.

A. Evgrafov, On Chebyshevs method for topology optimization of Stokes flows. Structural and Multidisciplinary Optimization, pp.801-811, 2015.

G. P. Galdi, An introduction to the mathematical theory of the Navier-Stokes equations: Steady-state problems, 2011.

M. J. Gander, L. Halpern, C. Japhet, and V. Martin, Viscous Problems with Inviscid Approximations in Subregions: a New Approach Based on Operator Factorization, ESAIM: Proceedings, pp.272-288, 2009.
DOI : 10.1051/proc/2009032

F. Gastaldi, A. Quarteroni, and G. S. Landriani, Coupling of two-dimensional hyperbolic and elliptic equations, Computer Methods in Applied Mechanics and Engineering, vol.80, issue.1-3, 1989.
DOI : 10.1016/0045-7825(90)90039-O

A. R. Gersborg, Topology optimization of flow problems, 2007.

V. Girault and P. A. Raviart, Finite element methods for Navier-Stokes equations: theory and algorithms, Comput. Math, vol.5, 1986.
DOI : 10.1007/978-3-642-61623-5

V. Girault and B. &rivì-ere, DG Approximation of Coupled Navier???Stokes and Darcy Equations by Beaver???Joseph???Saffman Interface Condition, SIAM Journal on Numerical Analysis, vol.47, issue.3, pp.2052-2089, 2009.
DOI : 10.1137/070686081

M. D. Gunzburger, L. Hou, and T. P. Svobodny, Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with distributed and Neumann controls, Mathematics of Computation, vol.57, issue.195, pp.57-123, 1991.
DOI : 10.1090/S0025-5718-1991-1079020-5

M. D. Gunzburger, Perspectives in flow control and optimization Siam, 2003.
DOI : 10.1115/1.1623758

F. Hecht, New development in freefem++, Journal of Numerical Mathematics, vol.20, issue.3-4, 2012.
DOI : 10.1515/jnum-2012-0013
URL : https://hal.archives-ouvertes.fr/hal-01476313

R. Herzog and K. Kunisch, Algorithms for PDE-constrained optimization, GAMM-Mitteilungen, vol.46, issue.4, pp.163-176, 2010.
DOI : 10.1137/S1052623400371569

M. Hinze, R. Pinnau, M. Ulbrich, and S. Ulbrich, Optimization with PDE constraints, 2008.

W. Jäger and A. Mikeli´cmikeli´c, Modeling effective interface laws for transport phenomena between an unconfined fluid and a porous medium using homogenization, Transport in Porous Media, pp.489-508, 2009.

C. Othmer, A continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flows, International Journal for Numerical Methods in Fluids, vol.18, issue.4, pp.861-877, 2008.
DOI : 10.1007/978-3-642-87722-3

K. I. Tujin, Regularity of Solutions to the Navier-Stokes Equations with a Nonstandard Boundary Condition, Acta Mathematicae Applicatae Sinica, vol.3, p.10, 2015.

N. Petra and G. Stadler, Model variational inverse problems governed by partial differential equations (No. ICES- 11-05), TEXAS UNIV AT AUSTIN INST FOR COMPUTATIONAL ENGINEERING AND SCIENCES, 2011.
DOI : 10.21236/ada555315

X. Qian and E. M. Dede, Topology optimization of a coupled thermal-fluid system under a tangential thermal gradient constraint. Structural and Multidisciplinary Optimization, pp.531-551, 2016.

J. P. Raymond, Stokes and NavierStokes equations with nonhomogeneous boundary conditions, Annales de l'IHP Analyse non linaire, pp.921-951, 2007.
DOI : 10.1016/j.anihpc.2006.06.008
URL : https://hal.archives-ouvertes.fr/hal-00635923

J. E. Roberts and J. M. Thomas, Mixed and Hybrid Methods, Handbook of Numerical Anaysis, p.184, 1993.

R. Temam, Navier Stokes Equations: Theory and Numerical Analysis, Journal of Applied Mechanics, vol.45, issue.2, 2001.
DOI : 10.1115/1.3424338

N. Wiker, A. Klarbring, and T. Borrvall, Topology optimization of regions of Darcy and Stokes flow, International Journal for Numerical Methods in Engineering, vol.66, issue.7, pp.1374-1404, 2007.
DOI : 10.1007/978-1-4612-3172-1