]. L. Afraites, M. Dambrine, and D. Kateb, Shape Methods for the Transmission Problem with a Single Measurement, Numerical Functional Analysis and Optimization, vol.25, issue.5-6, pp.5-6519, 2007.
DOI : 10.1137/S0036141096299375

L. Afraites, M. Dambrine, and D. Kateb, On Second Order Shape Optimization Methods for Electrical Impedance Tomography, SIAM Journal on Control and Optimization, vol.47, issue.3, pp.1556-1590, 2008.
DOI : 10.1137/070687438
URL : https://hal.archives-ouvertes.fr/hal-00140211

F. Alauzet, B. Mohammadi, and O. Pironneau, Mesh Adaptivity and Optimal Shape Design for Aerospace, Variational Analysis and Aerospace Engineering: Mathematical Challenges for Aerospace Design, pp.323-337, 2012.
DOI : 10.1007/978-1-4614-2435-2_14

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

H. Ammari, E. Bossy, J. Garnier, and L. Seppecher, Acousto-electromagnetic Tomography, SIAM Journal on Applied Mathematics, vol.72, issue.5, pp.1592-1617, 2012.
DOI : 10.1137/120863654
URL : https://hal.archives-ouvertes.fr/hal-00778971

H. Azegami, S. Kaizu, M. Shimoda, and E. Katamine, Irregularity of shape optimization problems and an improvement technique, Computer Aided Optimization Design of Structures V, pp.309-326, 1997.

N. Banichuk, F. Barthold, A. Falk, and E. Stein, Mesh refinement for shape optimization, Structural Optimization, vol.32, issue.1, pp.46-51, 1995.
DOI : 10.1007/BF01742644

L. Borcea, Electrical impedance tomography, Inverse Problems, vol.18, issue.6, p.99, 2002.
DOI : 10.1088/0266-5611/18/6/201

A. Calderón, On an inverse boundary value problem, Seminar on Numerical Analysis and its Applications to Continuum Physics, pp.65-73, 1980.
DOI : 10.1590/S0101-82052006000200002

A. Carpio and M. Rapún, Hybrid topological derivative and gradient-based methods for electrical impedance tomography, Inverse Problems, vol.28, issue.9, p.95010, 2012.
DOI : 10.1088/0266-5611/28/9/095010

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.371-402, 1986.
DOI : 10.1051/m2an/1986200303711

M. Cheney, D. Isaacson, and J. Newell, Electrical Impedance Tomography, SIAM Review, vol.41, issue.1, pp.85-101, 1999.
DOI : 10.1137/S0036144598333613

E. Chung, T. Chan, and X. Tai, Electrical impedance tomography using level set representation and total variational regularization, Journal of Computational Physics, vol.205, issue.1, pp.357-372, 2005.
DOI : 10.1016/j.jcp.2004.11.022

M. Delfour and J. Zolésio, Shapes and geometries: analysis, differential calculus, and optimization, SIAM, 2001.
DOI : 10.1137/1.9780898719826

G. Dog?andog?an, P. Morin, R. Nochetto, and M. Verani, Discrete gradient flows for shape optimization and applications, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.37-40, pp.3898-3914, 2007.
DOI : 10.1016/j.cma.2006.10.046

K. Eppler and H. Harbrecht, A regularized Newton method in electrical impedance tomography using shape Hessian information, Control Cybernet, vol.34, issue.1, pp.203-225, 2005.

L. Formaggia, S. Micheletti, and S. Perotto, Anisotropic mesh adaptation in computational fluid dynamics: Application to the advection???diffusion???reaction and the Stokes problems, Applied Numerical Mathematics, vol.51, issue.4, pp.511-533, 2004.
DOI : 10.1016/j.apnum.2004.06.007

T. Grätsch and K. Bathe, Goal-oriented error estimation in the analysis of fluid flows with structural interactions, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.41-43, pp.5673-5684, 2006.
DOI : 10.1016/j.cma.2005.10.020

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

M. Hintermüller and A. Laurain, Electrical impedance tomography: from topology to shape, Control Cybern, vol.37, issue.4, pp.913-933, 2008.

M. Hintermüller, A. Laurain, and A. A. Novotny, Second-order topological expansion for electrical impedance tomography, Advances in Computational Mathematics, vol.37, issue.4, pp.235-265, 2012.
DOI : 10.1007/s10444-011-9205-4

R. Hiptmair, A. Paganini, and S. Sargheini, Comparison of approximate shape gradients, BIT Numerical Mathematics, vol.85, issue.5, pp.1-27, 2014.
DOI : 10.1007/s10543-014-0515-z

D. Holder, Electrical Impedance Tomography: Methods, History and Applications. Series in Medical Physics and Biomedical Engineering, 2004.
DOI : 10.1201/9781420034462

B. Jin and P. Maass, An analysis of electrical impedance tomography with applications to Tikhonov regularization, ESAIM: Control, Optimisation and Calculus of Variations, vol.18, issue.4, pp.1027-1048, 2012.
DOI : 10.1051/cocv/2011193

N. Kikuchi, K. Chung, T. Torigaki, and J. Taylor, Adaptive Finite Element Methods for Shape Optimization of Linearly Elastic Structures, Comput. Method Appl. Mech. Eng, vol.57, pp.67-89, 1986.
DOI : 10.1007/978-1-4615-9483-3_6

R. Kohn and M. Vogelius, Relaxation of a variational method for impedance computed tomography, Communications on Pure and Applied Mathematics, vol.34, issue.6, pp.745-777, 1987.
DOI : 10.1002/cpa.3160400605

A. Laurain and K. Sturm, Distributed shape derivative via averaged adjoint method and applications, M2AN Math. Model. Numer. Anal, 2015.

P. Morin, R. Nochetto, M. Pauletti, and M. Verani, Adaptive finite element method for shape optimization, ESAIM: Control, Optimisation and Calculus of Variations, vol.18, issue.4, pp.1122-1149, 2012.
DOI : 10.1051/cocv/2011192

J. Oden and S. Prudhomme, Goal-oriented error estimation and adaptivity for the finite element method, Computers & Mathematics with Applications, vol.41, issue.5-6, pp.5-6735, 2001.
DOI : 10.1016/S0898-1221(00)00317-5

O. Pantz, Sensibilité de l'´ equation de la chaleur aux sauts de conductivité, C. R. Acad. Sci. Paris, Ser. I, issue.341, pp.333-337, 2005.

G. Porta, S. Perotto, and F. Ballio, Anisotropic mesh adaptation driven by a recovery-based error estimator for shallow water flow modeling, International Journal for Numerical Methods in Fluids, vol.30, issue.6, pp.269-299, 2012.
DOI : 10.1002/fld.2688

S. Prudhomme, J. Oden, T. Westermann, J. Bass, and M. Botkin, Practical methods fora posteriori error estimation in engineering applications, International Journal for Numerical Methods in Engineering, vol.47, issue.8, pp.1193-1224, 2003.
DOI : 10.1002/nme.609

S. Repin, A posteriori error estimation for variational problems with uniformly convex functionals, Mathematics of Computation, vol.69, issue.230, pp.481-500, 2000.
DOI : 10.1090/S0025-5718-99-01190-4

J. Roche, Adaptive Newton-like method for shape optimization, Control Cybern, vol.34, issue.1, pp.363-377, 2005.

M. Rüter, T. Gerasimov, and E. Stein, Goal-oriented explicit residual-type error estimates in XFEM, Computational Mechanics, vol.195, issue.2, pp.361-376, 2013.
DOI : 10.1007/s00466-012-0816-5

A. Schleupen, K. Maute, and E. Ramm, Adaptive FE-procedures in shape optimization, Structural and Multidisciplinary Optimization, vol.19, issue.4, pp.282-302, 2000.
DOI : 10.1007/s001580050125

J. Soko-lowski and J. Zolésio, Introduction to shape optimization: shape sensitivity analysis, 1992.

J. Sylvester and G. Uhlmann, A Global Uniqueness Theorem for an Inverse Boundary Value Problem, The Annals of Mathematics, vol.125, issue.1, pp.153-169, 1987.
DOI : 10.2307/1971291

T. Vejchodsk´yvejchodsk´y, Complementary error bounds for elliptic systems and applications, Appl. Math. Comput, vol.219, issue.13, pp.7194-7205, 2013.

A. Wexler, B. Fry, and M. R. Neuman, Impedance-computed tomography algorithm and system, Applied Optics, vol.24, issue.23, pp.3985-3992, 1985.
DOI : 10.1364/AO.24.003985