R. Albanese, J. Blum, and O. Barbieri, On the solution of the magnetic flux equation in an infinite domain, EPS. 8th Europhysics Conference on Computing in Plasma Physics, 1986.

R. Albanese, J. Blum, and O. De-barbieri, Numerical studies of the Next European Torus via the PROTEUS code, 12th Conf. on Numerical Simulation of Plasmas, 1987.

R. Albanese and F. Villone, The linearized CREATE-L plasma response model for the control of current, position and shape in tokamaks, Nuclear Fusion, vol.38, issue.5, p.723, 1998.
DOI : 10.1088/0029-5515/38/5/307

J. M. Ané, V. Grandgirard, F. Albajar, and J. Johner, Design of next step tokamak: Consistent analysis of plasma performance flux composition and poloidal field system, 18th IAEA Fusion Energy Conference, 2000.

M. Ariola and A. Pironti, Magnetic Control of Tokamak Plasmas, 2008.
DOI : 10.1007/978-3-319-29890-0

J. F. Artaud, V. Basiuk, F. Imbeaux, M. Schneider, J. Garcia et al., The CRONOS suite of codes for integrated tokamak modelling, The CRONOS suite of codes for integrated tokamak modelling, p.43001, 2010.
DOI : 10.1088/0029-5515/50/4/043001

J. Bielak and R. C. Maccamy, Symmetric finite element and boundary integral coupling methods for fluid-solid interaction, Quarterly of Applied Mathematics, vol.49, issue.1, pp.107-119, 1991.
DOI : 10.1090/qam/1096235

J. Blum, Numerical simulation of the plasma equilibrium in a Tokamak, Computer Physics Reports, vol.6, issue.1-6, 1987.
DOI : 10.1016/0167-7977(87)90015-3

J. Blum, C. Boulbe, and B. Faugeras, Reconstruction of the equilibrium of the plasma in a Tokamak and identification of the current density profile in real time, Journal of Computational Physics, vol.231, issue.3, pp.960-980
DOI : 10.1016/j.jcp.2011.04.005

URL : https://hal.archives-ouvertes.fr/hal-00419608

J. Blum and H. Heumann, 2014 Optimal control for quasi-static evolution of plasma equilibrium in tokamaks, Tech. Rep.. INRIA

J. Blum, L. Foll, J. Thooris, and B. , The self-consistent equilibrium and diffusion code sced, Computer Physics Communications, vol.24, issue.3-4, pp.235-254, 1981.
DOI : 10.1016/0010-4655(81)90149-1

. Chen, &. Goong, and . Zhou, Jianxin 1992 Boundary element methods

P. G. Ciarlet, The Finite Element Method for Elliptic Problems, studies in Mathematics and its Applications, 1978.

W. A. Cooper, S. P. Hirshman, P. Merkel, J. P. Graves, J. Kisslinger et al., Three-dimensional anisotropic pressure free boundary equilibria, Three-dimensional anisotropic pressure free boundary equilibria, pp.1524-1533, 2009.
DOI : 10.1016/j.cpc.2009.04.006

M. Costabel and E. P. Stephan, Coupling of Finite and Boundary Element Methods for an Elastoplastic Interface Problem, SIAM Journal on Numerical Analysis, vol.27, issue.5, pp.1212-1226, 1990.
DOI : 10.1137/0727070

L. M. Degtyarev and V. V. Drozdov, An inverse variable technique in the MHD-equilibrium problem, Computer Physics Reports, vol.2, issue.7, pp.341-387, 1985.
DOI : 10.1016/0167-7977(85)90002-4

L. M. Degtyarev and V. V. Drozdov, Adaptive Mesh Computation of Magnetic Hydrodynamic Equilibrium, International Journal of Modern Physics C, vol.02, issue.01, pp.2-30, 1991.
DOI : 10.1142/S0129183191000056

M. C. Delfour and J. Zolésio, 2011 Shapes and geometries, Advances in Design and Control

J. Delucia, S. C. Jardin, and A. M. Todd, An iterative metric method for solving the inverse tokamak equilibrium problem, Journal of Computational Physics, vol.37, issue.2, pp.183-204, 1980.
DOI : 10.1016/0021-9991(80)90020-0

G. L. Falchetto, D. Coster, R. Coelho, B. D. Scott, L. Figini et al., The European Integrated Tokamak Modelling (ITM) effort: achievements and first physics results, Contributors, ITM- TF, the ASDEX Upgrade Team & Contributors, JET-EFDA 2014 The European Integrated Tokamak Modelling (ITM) effort: achievements and first physics results, p.43018
DOI : 10.1088/0029-5515/54/4/043018

URL : https://hal.archives-ouvertes.fr/hal-01105065

. Feistauer, &. Miloslav, and . Sobotkov, Finite element approximation of nonlinear elliptic problems with discontinuous coefficients, ESAIM: Mathematical Modelling and Numerical Analysis, vol.24, issue.4, pp.457-500
DOI : 10.1051/m2an/1990240404571

W. Feneberg, K. Lackner, M. Fitzgerald, L. C. Appel, and M. J. Hole, Multipole tokamak equilibria 2013 EFIT tokamak equilibria with toroidal flow and anisotropic pressure using the two-temperature guiding-centre plasma, Nuclear Fusion Nuclear Fusion, vol.13, issue.5311, p.113040, 1973.

G. N. Gatica and G. C. Hsiao, The Uncoupling of Boundary Integral and Finite Element Methods for Nonlinear Boundary Value Problems, Journal of Mathematical Analysis and Applications, vol.189, issue.2, pp.442-461, 1995.
DOI : 10.1006/jmaa.1995.1029

R. Glowinski and A. Marrocco, Analyse numerique du champ magnetique d'un alternateur par elements finis et sur-relaxation ponctuelle non lineaire, Computer Methods in Applied Mechanics and Engineering, vol.3, issue.1, pp.55-85, 1974.
DOI : 10.1016/0045-7825(74)90042-5

J. P. Goedbloed and A. Lifschitz, Stationary symmetric magnetohydrodynamic flows, Physics of Plasmas, vol.4, issue.10, pp.3544-3564, 1994.
DOI : 10.1063/1.872251

J. P. Goedbloed, . Keppens, &. Rony, and . Poedts, Stefaan 2010 Advanced magnetohydrodynamics: with applications to laboratory and astrophysical plasmas
DOI : 10.1017/cbo9781139195560

J. Goedbloed, &. Peter, and . Poedts, Stefaan 2004 Principles of magnetohydrodynamics: with applications to laboratory and astrophysical plasmas

H. Grad, Toroidal Containment of a Plasma, Physics of Fluids, vol.10, issue.1, pp.137-154, 1958.
DOI : 10.1063/1.1761965

H. Grad and H. Rubin, Hydromagnetic equilibria and force-free fields, Proceedings of the 2nd UN Conf. on the Peaceful Uses of Atomic Energy 31, 0190.
DOI : 10.1016/0891-3919(58)90139-6

. Grandgirard, Virginie 1999 Modélisation de l'´ equilibre d'un plasma de tokamak

R. Gruber, R. Iacono, and F. Troyon, Computation of MHD equilibria by a quasi-inverse finite hybrid element approach, Journal of Computational Physics, vol.73, issue.1, pp.168-182, 1987.
DOI : 10.1016/0021-9991(87)90112-4

L. Guazzotto, R. Betti, J. Manickam, and S. Kaye, Numerical study of tokamak equilibria with arbitrary flow, Physics of Plasmas, vol.11, issue.2, pp.604-614, 1994.
DOI : 10.1063/1.1637918

F. J. Helton and T. S. Wang, MHD equilibrium in non-circular tokamaks with field-shaping coil systems, Nuclear Fusion, vol.18, issue.11, p.1523, 1978.
DOI : 10.1088/0029-5515/18/11/005

P. Hertout, C. Boulbe, E. Nardon, J. Blum, S. Bremond et al., The CEDRES++ equilibrium code and its application to ITER, JT-60SA and Tore Supra, Fusion Engineering and Design, vol.86, issue.6-8, pp.2011-1045
DOI : 10.1016/j.fusengdes.2011.03.092

URL : https://hal.archives-ouvertes.fr/hal-00872280

F. L. Hinton and R. D. Hazeltine, Theory of plasma transport in toroidal confinement systems, Reviews of Modern Physics, vol.48, issue.2, pp.239-308, 1976.
DOI : 10.1103/RevModPhys.48.239

R. Hiptmair, Coupling of Finite Elements and Boundary Elements in Electromagnetic Scattering, SIAM Journal on Numerical Analysis, vol.41, issue.3, pp.919-944, 2003.
DOI : 10.1137/S0036142901397757

S. P. Hirshman and O. Betancourt, Preconditioned descent algorithm for rapid calculations of magnetohydrodynamic equilibria, Journal of Computational Physics, vol.96, issue.1, pp.99-109, 1991.
DOI : 10.1016/0021-9991(91)90267-O

S. P. Hirshman and S. C. Jardin, Two-dimensional transport of tokamak plasmas, Physics of Fluids, vol.22, issue.4, pp.731-742, 1979.
DOI : 10.1063/1.862654

F. Hofmann and G. Tonetti, Tokamak equilibrium reconstruction using Faraday rotation measurements, Nuclear Fusion, vol.28, issue.10, p.1871, 1988.
DOI : 10.1088/0029-5515/28/10/014

URL : http://infoscience.epfl.ch/record/120899

G. T. Huysmans and O. Czarny, MHD stability in X-point geometry: simulation of ELMs, Nuclear Fusion, vol.47, issue.7, p.659, 2007.
DOI : 10.1088/0029-5515/47/7/016

G. T. Huysmans, J. P. Goedbloed, and W. Kerner, Isoparametric Bicubic Hermite Elements for Solution of the Grad-Shafranov Equation, Proc. CP90 Conf. on Comp. Phys. p, p.371, 1991.
DOI : 10.1142/S0129183191000512

S. C. Jardin, Computational methods in plasma physics, 2010.
DOI : 10.1201/EBK1439810958

S. C. Jardin, N. Pomphrey, and J. Delucia, Dynamic modeling of transport and positional control of tokamaks, Journal of Computational Physics, vol.66, issue.2, pp.481-507, 1986.
DOI : 10.1016/0021-9991(86)90077-X

J. L. Johnson, H. E. Dalhed, J. M. Greene, R. C. Grimm, Y. Y. Hsieh et al., Numerical determination of axisymmetric toroidal magnetohydrodynamic equilibria, Numerical determination of axisymmetric toroidal magnetohydrodynamic equilibria, pp.212-234, 1979.
DOI : 10.1016/0021-9991(79)90129-3

K. Lackner, Computation of ideal MHD equilibria, Computer Physics Communications, vol.12, issue.1, pp.33-44, 1976.
DOI : 10.1016/0010-4655(76)90008-4

L. L. Lao, J. R. Ferron, R. J. Geoebner, W. Howl, . St et al., Equilibrium analysis of current profiles in tokamaks, Nuclear Fusion, vol.30, issue.6, p.1035, 1990.
DOI : 10.1088/0029-5515/30/6/006

L. L. Lao, S. P. Hirshman, and R. M. Wieland, Variational moment solutions to the Grad???Shafranov equation, Physics of Fluids, vol.24, issue.8, pp.1431-1440, 1981.
DOI : 10.1063/1.863562

L. L. Lao, H. John, . St, R. D. Stambaugh, A. G. Kellman et al., Reconstruction of current profile parameters and plasma shapes in tokamaks, Nuclear Fusion, vol.25, issue.11, p.1611, 1985.
DOI : 10.1088/0029-5515/25/11/007

J. Li, J. Melenk, . Markus, . Wohlmuth, &. Barbara et al., Optimal a priori estimates for higher order finite elements for elliptic interface problems, Applied Numerical Mathematics, vol.60, issue.1-2, pp.19-37, 2010.
DOI : 10.1016/j.apnum.2009.08.005

K. M. Ling and S. C. Jardin, The Princeton spectral equilibrium code: PSEC, Journal of Computational Physics, vol.58, issue.3, pp.300-335, 1985.
DOI : 10.1016/0021-9991(85)90165-2

J. L. Luxon and B. B. Brown, Magnetic analysis of non-circular cross-section tokamaks, Nuclear Fusion, vol.22, issue.6, p.813, 1982.
DOI : 10.1088/0029-5515/22/6/009

E. K. Maschke and H. J. Perrin, An analytic solution of the stationary MHD equations for a rotating toroidal plasma, Physics Letters A, vol.102, issue.3, pp.106-108, 1984.
DOI : 10.1016/0375-9601(84)90790-4

J. Nédélec, Acoustic and electromagnetic equations, Applied Mathematical Sciences, vol.144, 2001.

V. Parail, R. Albanese, R. Ambrosino, J. Artaud, K. Besseghir et al., Self-consistent simulation of plasma scenarios for ITER using a combination of 1.5D transport codes and free-boundary equilibrium codes, Self-consistent H. Heumann et. al. simulation of plasma scenarios for iter using a combination of 1.5d transport codes and free-boundary equilibrium codes, p.113002, 2013.
DOI : 10.1088/0029-5515/53/11/113002

W. Park, E. V. Belova, G. Y. Fu, X. Z. Tang, H. R. Strauss et al., Plasma simulation studies using multilevel physics models, Physics of Plasmas, vol.6, issue.5, pp.1796-1803, 1994.
DOI : 10.1063/1.873437

C. Pechstein and B. Jüttler, Monotonicity-preserving interproximation of B???H-curves, Journal of Computational and Applied Mathematics, vol.196, issue.1, pp.45-57, 2006.
DOI : 10.1016/j.cam.2005.08.021

V. D. Pustovitov, Anisotropic pressure effects on plasma equilibrium in toroidal systems, Plasma Physics and Controlled Fusion, vol.52, issue.6, p.65001, 2010.
DOI : 10.1088/0741-3335/52/6/065001

Y. Renard and J. Pommier, 2014 GetFEM++, an open-source finite element library

C. Schwab, p-and hp-finite element methods : theory and applications in solid and fluid mechanics, 2004.

V. D. Shafranov, On magnetohydrodynamical equilibrium configurations, Soviet Journal of Experimental and Theoretical Physics, vol.6, p.545, 1958.

J. R. Shewchuk, Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator, Applied Computational Geometry: Towards Geometric Engineering, 1996.
DOI : 10.1007/BFb0014497

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.40.9874

E. P. Stephan, Coupling of finite elements and boundary elements for some nonlinear interface problems, Computer Methods in Applied Mechanics and Engineering, vol.101, issue.1-3, pp.61-72, 1992.
DOI : 10.1016/0045-7825(92)90015-C

B. Turkington, A. Lifschitz, A. Eydeland, and J. Spruck, Multiconstrained variational problems in magnetohydrodynamics: Equilibrium and slow evolution, Journal of Computational Physics, vol.106, issue.2, pp.269-285, 1993.
DOI : 10.1016/S0021-9991(83)71107-1

K. Zhao, M. N. Vouvakis, and J. Lee, Solving electromagnetic problems using a novel symmetric FEM-BEM approach, IEEE Transactions on Magnetics, vol.42, issue.4, pp.583-586, 2006.
DOI : 10.1109/TMAG.2006.872489

W. Zwingmann, L. Eriksson, and P. Stubberfield, Equilibrium analysis of tokamak discharges with anisotropic pressure, Plasma Physics and Controlled Fusion, vol.43, issue.11, p.1441, 2001.
DOI : 10.1088/0741-3335/43/11/302