M. Ainsworth and J. T. Oden, A posteriori error estimation in finite element analysis, Computer Methods in Applied Mechanics and Engineering, vol.142, issue.1-2, pp.1-88, 1997.
DOI : 10.1016/S0045-7825(96)01107-3

G. Allaire, Conception optimale de structures, Mathématiques et Applications, vol.58, 2006.

G. Allaire, E. Bonnetier, G. Francfort, and F. Jouve, Shape optimization by the homogenization method, Numerische Mathematik, vol.76, issue.1, pp.27-68, 1997.
DOI : 10.1007/s002110050253

G. Allaire and C. Dapogny, A linearized approach to worst-case design in parametric and geometric shape optimization, Mathematical Models and Methods in Applied Sciences, vol.24, issue.11, 2014.
DOI : 10.1142/S0218202514500195
URL : https://hal.archives-ouvertes.fr/hal-00918896

G. Allaire, C. Dapogny, G. Delgado, and G. Michailidis, Multi-phase optimization via a level set method, to appear in ESAIM: Control, Optimisation and Calculus of Variations, 2014.

G. Allaire, C. Dapogny, and P. Frey, Topology and geometry optimization of elastic structures by exact deformation of simplicial mesh, Comptes Rendus Mathematique, vol.349, issue.17-18, pp.999-1003, 2011.
DOI : 10.1016/j.crma.2011.08.012
URL : https://hal.archives-ouvertes.fr/hal-00784047

G. Allaire, C. Dapogny, and P. Frey, A mesh evolution algorithm based on the level set method for geometry and topology optimization, Structural and Multidisciplinary Optimization, vol.87, issue.91, pp.711-715, 2013.
DOI : 10.1007/s00158-013-0929-2
URL : https://hal.archives-ouvertes.fr/hal-00801704

G. Allaire, F. De-gournay, F. Jouve, and A. M. Toader, Structural optimization using topological and shape sensitivity analysis via a level-set method, Control and Cybernetics, vol.34, pp.59-80, 2005.

G. Allaire and F. Jouve, A level-set method for vibration and multiple loads structural optimization, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.30-33, pp.3269-3290, 2005.
DOI : 10.1016/j.cma.2004.12.018

G. Allaire and F. Jouve, Minimum stress optimal design with the level set method, Engineering Analysis with Boundary Elements, pp.909-918, 2008.

G. Allaire, F. Jouve, and A. M. Toader, Structural optimization using sensitivity analysis and a level-set method, Journal of Computational Physics, vol.194, issue.1, pp.363-393, 2004.
DOI : 10.1016/j.jcp.2003.09.032

G. Allaire, F. Jouve, and N. Van-goethem, Damage and fracture evolution in brittle materials by shape optimization methods, Journal of Computational Physics, vol.230, issue.12, pp.5010-5044, 2011.
DOI : 10.1016/j.jcp.2011.03.024
URL : https://hal.archives-ouvertes.fr/hal-00784048

G. Allaire and O. Pantz, Structural optimization with $\tt{FreeFem++}$, Structural and Multidisciplinary Optimization, vol.21, issue.1, pp.173-181, 2006.
DOI : 10.1007/s00158-006-0017-y

J. F. Aujol and G. Aubert, Signed distance functions and viscosity solutions of discontinuous Hamilton-Jacobi Equations, INRIA Technical Report, p.4507, 2002.
URL : https://hal.archives-ouvertes.fr/inria-00072081

T. J. Baker, Mesh Movement and Metamorphosis, Engineering with Computers, vol.18, issue.3, pp.188-198, 2002.
DOI : 10.1007/s003660200017
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.11.9161

M. P. Bendsøe and N. Kikuchi, Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, vol.71, issue.2, pp.197-224, 1988.
DOI : 10.1016/0045-7825(88)90086-2

M. P. Bendsøe and O. Sigmund, Topology Optimization, Theory, Methods and Applications, 2003.

B. Bourdin and A. Chambolle, Design-dependent loads in topology optimization, ESAIM: Control, Optimisation and Calculus of Variations, vol.9, pp.19-48, 2003.
DOI : 10.1051/cocv:2002070

V. Braibant and C. Fleury, Shape optimal design using B-splines, Computer Methods in Applied Mechanics and Engineering, vol.44, issue.3, pp.247-267, 1984.
DOI : 10.1016/0045-7825(84)90132-4

C. Bui, C. Dapogny, and P. Frey, An accurate anisotropic adaptation method for solving the level set advection equation, International Journal for Numerical Methods in Fluids, vol.110, issue.7, pp.899-922, 2012.
DOI : 10.1002/fld.2730

M. Burger, A framework for the construction of level-set methods for shape optimization and reconstruction, Interfaces and Free Boundaries, pp.301-329, 2003.

M. Burger, B. Hackl, and W. Ring, Incorporating topological derivatives into level set methods, Journal of Computational Physics, vol.194, issue.1, pp.344-362, 2004.
DOI : 10.1016/j.jcp.2003.09.033
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.9.8456

J. Céa, Conception optimale ou identification de formes, calcul rapide de la d??riv??e directionnelle de la fonction co??t, ESAIM: Mathematical Modelling and Numerical Analysis, vol.20, issue.3, pp.371-420, 1986.
DOI : 10.1051/m2an/1986200303711

A. Cherkaev and E. Cherkaeva, Principal Compliance and Robust Optimal Design, Journal of Elasticity, vol.72, issue.1-3, pp.71-98, 2003.
DOI : 10.1023/B:ELAS.0000018772.09023.6c

D. Chopp, Computing Minimal Surfaces via Level Set Curvature Flow, Journal of Computational Physics, vol.106, issue.1, pp.77-91, 1993.
DOI : 10.1006/jcph.1993.1092

A. N. Christiansen, M. Nobel-jørgensen, N. Aage, O. Sigmund, and J. A. Baerentzen, Topology optimization using an explicit interface representation, to appear in Struct, Multidisc. Optim, 2013.

P. G. Ciarlet, The Finite Element Method for Elliptic Problems, 1978.

C. Dapogny, C. Dobrzynski, and P. Frey, Three-dimensional adaptive domain remeshing, implicit domain meshing, and applications to free and moving boundary problems, Journal of Computational Physics, vol.262, 2013.
DOI : 10.1016/j.jcp.2014.01.005
URL : https://hal.archives-ouvertes.fr/hal-01110395

C. Dapogny and P. Frey, Computation of the signed distance function to a discrete contour on adapted triangulation, Calcolo, pp.193-219, 2012.

J. D. Deaton and R. V. Grandhi, A survey of structural and multidisciplinary continuum topology optimization, Struct. Multidisc. Optim, 2000.

M. C. Delfour and J. Zolesio, Shapes and Geometries: Metrics, Analysis, Differential Calculus, and Optimization, 2011.
DOI : 10.1137/1.9780898719826

N. P. Van-dijk, K. Maute, M. Langelaar, and F. Van-keulen, Level-set methods for structural topology optimization: a review, Structural and Multidisciplinary Optimization, vol.42, issue.9
DOI : 10.1007/s00158-013-0912-y

C. Dobrzynski, Adaptation de maillage anisotrope 3d et applicationàapplicationà l'aéro-thermique des bâtiments, Thèse de l, 2005.

C. Dobrzynski and P. Frey, Anisotropic Delaunay Mesh Adaptation for Unsteady Simulations, Proc. 17th Int. Meshing Roundtable, 2008.
DOI : 10.1007/978-3-540-87921-3_11
URL : https://hal.archives-ouvertes.fr/hal-00353786

P. Duysinx, L. Van-miegroet, T. Jacobs, and C. Fleury, Generalized Shape Optimization Using X-FEM and Level Set Methods, IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials Solid Mechanics and Its Applications, pp.23-32, 2006.
DOI : 10.1007/1-4020-4752-5_3
URL : http://orbi.ulg.ac.be/jspui/handle/2268/18129

H. Eschenauer, V. Kobelev, and A. Schumacher, Bubble method for topology and shape optimization of structures, Structural Optimization, pp.42-51, 1994.

L. Freitag and C. Olliver-gooch, Tetrahedral mesh improvement using swapping and smoothing, International Journal for Numerical Methods in Engineering, vol.5, issue.21, pp.3979-4002, 1997.
DOI : 10.1002/(SICI)1097-0207(19971115)40:21<3979::AID-NME251>3.0.CO;2-9

P. Frey and H. Borouchaki, Texel : triangulation de surfaces implicites. Partie I : aspects théoriques., INRIA, p.3066, 1996.
URL : https://hal.archives-ouvertes.fr/inria-00073626

P. J. Frey and P. L. George, Mesh Generation : Application to Finite Elements, 2008.
DOI : 10.1002/9780470611166

S. Garreau, P. Guillaume, and M. Masmoudi, The Topological Asymptotic for PDE Systems: The Elasticity Case, SIAM Journal on Control and Optimization, vol.39, issue.6, pp.1756-1778, 2001.
DOI : 10.1137/S0363012900369538

P. George and H. Borouchaki, Back to edge flips in 3 dimensions, Proc. 12th Int. Meshing Roundtable, 2003.

F. De-gournay, Velocity Extension for the Level-set Method and Multiple Eigenvalues in Shape Optimization, SIAM Journal on Control and Optimization, vol.45, issue.1, pp.343-367, 2006.
DOI : 10.1137/050624108

F. De-gournay, G. Allaire, and F. Jouve, Shape and topology optimization of the robust compliance via the level set method, ESAIM: Control, Optimization and Calculus of Variations, pp.43-70, 2008.

S. Ha and S. Cho, Level set based topological shape optimization of geometrically nonlinear structures using unstructured mesh, Computers and Structures, pp.844-868, 2008.

F. Hecht, New development in freefem++, Journal of Numerical Mathematics, vol.20, issue.3-4, pp.251-265, 2012.
DOI : 10.1515/jnum-2012-0013

A. Henrot and M. Pierre, Variation et Optimisation de Formes : une Etude Géométrique, Mathématiques et Applications, vol.48, 2005.
DOI : 10.1007/3-540-37689-5

L. Li, M. Y. Wang, and P. Wei, XFEM schemes for level set based structural optimization, Front, Mech. Eng, pp.335-356, 2012.

W. E. Lorensen and H. E. Cline, Marching cubes: A high resolution 3D surface construction algorithm, ACM SIGGRAPH Computer Graphics, vol.21, issue.4, pp.163-169, 1987.
DOI : 10.1145/37402.37422

M. K. Misztal and J. A. Baerentzen, Topology-adaptive interface tracking using the deformable simplicial complex, ACM Transactions on Graphics, vol.31, issue.3, pp.1-24, 2012.
DOI : 10.1145/2167076.2167082

F. Murat and J. Simon, Sur le contrôle par un domaine géométrique, 1976.

S. J. Osher and F. Santosa, Level Set Methods for Optimization Problems Involving Geometry and Constraints, Journal of Computational Physics, vol.171, issue.1, pp.272-288, 2001.
DOI : 10.1006/jcph.2001.6789

S. J. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988.
DOI : 10.1016/0021-9991(88)90002-2

P. Persson, Mesh Generation for Implicit Geometries, 2004.

O. Pironneau, On optimum profiles in Stokes flow, Journal of Fluid Mechanics, vol.none, issue.01, pp.117-128, 1973.
DOI : 10.1017/S002211207300145X

O. Pironneau, The finite element methods for fluids, 1989.

J. A. Sethian, Level Set Methods and Fast Marching Methods : Evolving Interfaces in Computational Geometry,Fluid Mechanics, Computer Vision, and Materials Science, 1999.

J. A. Sethian and A. Wiegmann, Structural Boundary Design via Level Set and Immersed Interface Methods, Journal of Computational Physics, vol.163, issue.2, pp.489-528, 2000.
DOI : 10.1006/jcph.2000.6581

J. Sokolowski and J. Zolesio, Introduction to Shape Optimization : Shape Sensitivity Analysis, Comput. Math, vol.10, 1992.

J. Strain, Semi-Lagrangian Methods for Level Set Equations, Journal of Computational Physics, vol.151, issue.2, pp.498-533, 1999.
DOI : 10.1006/jcph.1999.6194

L. A. Vese and T. F. Chan, A multiphase level set framework for image segmentation using the Mumford and Shah model, International Journal of Computer Vision, vol.50, issue.3, pp.271-293, 2002.
DOI : 10.1023/A:1020874308076

M. Y. Wang, X. Wang, and D. Guo, A level set method for structural topology optimization, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.1-2, pp.227-246, 2003.
DOI : 10.1016/S0045-7825(02)00559-5

Q. Xia, T. Shi, S. Liu, and M. Y. Wang, A level set solution to the stress-based structural shape and topology optimization, Computers and Structures, pp.90-91, 2012.

S. Yamasaki, T. Nomura, A. Kawamoto, and S. Nishiwaki, A level set-based topology optimization method targeting metallic waveguide design problems, International Journal for Numerical Methods in Engineering, vol.41, issue.5, pp.844-868, 2011.
DOI : 10.1002/nme.3135

O. C. Zienkiewicz and J. S. Campbell, Shape optimization and sequential linear programming, pp.109-126, 1973.