H. Akima, A method of bivariate interpolation and smooth surface fitting based on local procedures, Communications of the ACM, vol.17, issue.1, pp.18-20, 1974.
DOI : 10.1145/360767.360779

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, pp.41-44, 1986.

K. Bell, A refined triangular plate bending finite element, International Journal for Numerical Methods in Engineering, vol.93, issue.1, pp.101-122, 1969.
DOI : 10.1002/nme.1620010108

H. Berestycki and H. Brézis, On a free boundary problem arising in plasma physics, Nonlinear Analysis: Theory, Methods & Applications, vol.4, issue.3, pp.415-436, 1980.
DOI : 10.1016/0362-546X(80)90083-8

C. Bernardi, Y. Maday, and A. T. Patera, A new nonconforming approach to domain decomposition: the mortar element method In Nonlinear partial differential equations and their applications, Colì ege de France Seminar Pitman Res. Notes Math. Ser., Longman Sci. Tech, vol.299, pp.13-51, 1989.

M. Blommaert, M. Baelmans, W. Dekeyser, N. R. Gauger, and D. Reiter, A novel approach to magnetic divertor configuration design, Journal of Nuclear Materials, vol.463, pp.463-1220, 2015.
DOI : 10.1016/j.jnucmat.2014.11.053

M. Blommaert, H. Heumann, M. Baelmans, N. R. Gauger, and D. Reiter, Towards Automated Magnetic Divertor Design for Optimal Heat Exhaust, ESAIM: Proceedings and Surveys, vol.53, pp.53-102, 2016.
DOI : 10.1051/proc/201653004

URL : https://hal.archives-ouvertes.fr/hal-01389537

J. Blum, Numerical simulation and optimal control in plasma physics, 1989.

J. Blum, T. Gallouet, and J. Simon, Existence and Control of Plasma Equilibrium in a Tokamak, SIAM Journal on Mathematical Analysis, vol.17, issue.5, pp.1158-1177, 1986.
DOI : 10.1137/0517081

J. Blum and J. L. Foll, Plasma equilibrium evolution at the resistive diffusion timescale, Computer Physics Reports, vol.1, issue.7-8, pp.7-8, 1984.
DOI : 10.1016/0167-7977(84)90013-3

J. Blum, J. L. Foll, and B. Thooris, 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

F. K. Bogner, R. L. Fox, and L. A. Schmit, The generation of interelement compatible stiffness and mass matrices by the use of interpolation formulas, Proceedings of the Conference on Matrix Methods in Structural Mechanics, 1965.

X. Cai, M. Dryja, and M. Sarkis, Overlapping Nonmatching Grid Mortar Element Methods for Elliptic Problems, SIAM Journal on Numerical Analysis, vol.36, issue.2, pp.581-606, 1999.
DOI : 10.1137/S0036142997323582

L. Chen, Programming of finite element methods in Matlab, 2011.

A. Christophe, Y. Le-bihan, and F. Rapetti, A mortar element approach on overlapping nonnested grids: application to eddy current non-destructive testing, Appl. Math. Comput, vol.267, pp.71-82, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01254684

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

F. Cuvelier, C. Japhet, and G. Scarella, An efficient way to assemble finite element matrices in vector languages, BIT Numerical Mathematics, vol.219, issue.13, pp.833-864, 2016.
DOI : 10.1007/s10543-015-0587-4

URL : https://hal.archives-ouvertes.fr/hal-00931066

M. C. Delfour and J. Zolésio, Shapes and geometries, volume 22 of Advances in Design and Control, Society for Industrial and Applied Mathematics (SIAM), 2011.

L. Demkowicz, Computing with hp-adaptive finite elements One and two dimensional elliptic and Maxwell problems, CRC Applied Mathematics and Nonlinear Science Series. Chapman & Hall/CRC, vol.1, p.1, 2007.

B. Flemisch and B. I. Wohlmuth, A domain decomposition method on nested domains and nonmatching grids, Numerical Methods for Partial Differential Equations, vol.38, issue.3, pp.374-387, 2004.
DOI : 10.1002/num.10095

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

J. P. Goedbloed, R. Keppens, and S. Poedts, Advanced magnetohydrodynamics: with applications to laboratory and astrophysical plasmas, 2010.
DOI : 10.1017/CBO9781139195560

J. P. Goedbloed and S. Poedts, Principles of magnetohydrodynamics: with applications to laboratory and astrophysical plasmas, 2004.
DOI : 10.1017/CBO9780511616945

J. P. Goedbloed, Conformal mapping methods in two-dimensional magnetohydrodynamics, Computer Physics Communications, vol.24, issue.3-4, pp.3-4, 1981.
DOI : 10.1016/0010-4655(81)90153-3

H. Grad and J. Hogan, Classical Diffusion in a Tokomak, Physical Review Letters, vol.24, issue.24, pp.1337-1340, 1970.
DOI : 10.1103/PhysRevLett.24.1337

H. Grad and H. Rubin, Hydromagnetic equilibria and force-free fields, Proceedings of the 2nd UN Conf. on the Peaceful Uses of Atomic Energy, pp.190-197, 1958.
DOI : 10.1016/0891-3919(58)90139-6

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

H. Haddar and Z. Jiang, Axisymmetric eddy current inspection of highly conducting thin layers via asymptotic models, Inverse Problems, vol.31, issue.11, pp.1-25, 2015.
DOI : 10.1088/0266-5611/31/11/115005

URL : https://hal.archives-ouvertes.fr/hal-01214308

H. Haddar, Z. Jiang, and A. Lechleiter, Artificial boundary conditions for axisymmetric eddy current probe problems, Computers & Mathematics with Applications, vol.68, issue.12, pp.1844-1870, 2014.
DOI : 10.1016/j.camwa.2014.10.008

URL : https://hal.archives-ouvertes.fr/hal-01072091

F. Hecht, A. Lozinski, and O. Pironneau, Numerical Zoom and the Schwarz Algorithm, Lect. Notes Comput. Sci. Eng, vol.70, pp.63-73, 2009.
DOI : 10.1007/978-3-642-02677-5_6

URL : https://hal.archives-ouvertes.fr/hal-00628622

H. Heumann, J. Blum, C. Boulbe, B. Faugeras, G. Selig et al., Quasi-static free-boundary equilibrium of toroidal plasma with CEDRES++: Computational methods and applications, Journal of Plasma Physics, vol.6, issue.03, pp.1-35, 2015.
DOI : 10.1016/j.fusengdes.2011.03.092

URL : https://hal.archives-ouvertes.fr/hal-01088772

M. Honda, Simulation technique of free-boundary equilibrium evolution in plasma ramp-up phase, Computer Physics Communications, vol.181, issue.9, pp.1490-1500, 2010.
DOI : 10.1016/j.cpc.2010.04.014

E. C. Howell and C. R. Sovinec, Solving the Grad???Shafranov equation with spectral elements, Computer Physics Communications, vol.185, issue.5, pp.1415-1421, 2014.
DOI : 10.1016/j.cpc.2014.02.008

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, pp.371-372, 1991.
DOI : 10.1142/S0129183191000512

S. C. Jardin, A triangular finite element with first-derivative continuity applied to fusion MHD applications, Journal of Computational Physics, vol.200, issue.1, pp.133-152, 2004.
DOI : 10.1016/j.jcp.2004.04.004

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

G. E. Karniadakis and S. J. Sherwin, Spectral/hp element methods for computational fluid dynamics. Numerical Mathematics and Scientific Computation, 2005.

R. R. Khayrutdinov and V. E. Lukash, Studies of Plasma Equilibrium and Transport in a Tokamak Fusion Device with the Inverse-Variable Technique, Journal of Computational Physics, vol.109, issue.2, pp.193-201, 1993.
DOI : 10.1006/jcph.1993.1211

J. Koko, Vectorized matlab codes for linear two-dimensional elasticity. Sci. Program, pp.157-172, 2007.

Y. A. Kuznetsov, Overlapping domain decomposition with non-matching grids In Recent developments in domain decomposition methods and flow problems, GAKUTO Internat. Ser. Math. Sci. Appl. Gakk¯ otosho, vol.11, pp.62-71, 1996.

R. Lüst and A. Schlüter, Axialsymmetrische magnetohydrodynamische Gleichgewichtskonfigurationen, Zeitschrift f??r Naturforschung A, vol.12, issue.10, pp.850-854, 1957.
DOI : 10.1515/zna-1957-1014

J. L. Luxon and B. B. Brown, Magnetic analysis of non-circular cross-section tokamaks, Nuclear Fusion, vol.22, issue.6, pp.813-821, 1982.
DOI : 10.1088/0029-5515/22/6/009

H. Lütjens, A. Bondeson, and A. Roy, Axisymmetric MHD equilibrium solver with bicubic Hermite elements, Computer Physics Communications, vol.69, issue.2-3, pp.287-298, 1992.
DOI : 10.1016/0010-4655(92)90167-W

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

M. A. Nakamura, On an equilibrium of the plasma in a Tokamak with a limiter, Japan Journal of Industrial and Applied Mathematics, vol.2, issue.3, pp.431-444, 1991.
DOI : 10.1007/BF03167145

J. Nocedal and S. J. Wright, Numerical optimization. Springer Series in Operations Research and Financial Engineering, 2006.

A. Palha, B. Koren, and F. Felici, A mimetic spectral element solver for the gradshafranov equation, J. of Comput. Phys, pp.316-63, 2016.

A. Pataki, A. J. Cerfon, J. P. Freidberg, L. Greengard, and M. O. Neil, A fast, high-order solver for the Grad???Shafranov equation, Journal of Computational Physics, vol.243, issue.0, pp.28-45, 2013.
DOI : 10.1016/j.jcp.2013.02.045

]. 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

D. D. Ryutov, Geometrical properties of a ???snowflake??? divertor, Physics of Plasmas, vol.14, issue.6, p.14, 2007.
DOI : 10.1063/1.2738399

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.

V. D. Shafranov and L. E. Zakharov, Use of the virtual-casing principle in calculating the containing magnetic field in toroidal plasma systems, Nuclear Fusion, vol.12, issue.5, pp.599-601, 1972.
DOI : 10.1088/0029-5515/12/5/009

R. Temam, Remarks on a free Boundary Value Problem Arising in Plasma Physics, Communications in Partial Differential Equations, vol.51, issue.6, pp.563-585, 1977.
DOI : 10.1007/BF00281469

M. D. Truong, The mortar element method for the free-boundary toroidal plasma equilibrium problem, Erasmus Mundus Joint Master Degree in Mathematical Modeling in Engineering MATHMODS, 2016.

J. Wesson, Tokamaks. The International Series of Monographs in Physics, 2004.

B. I. Wohlmuth, Discretization methods and iterative solvers based on domain decomposition, Lecture Notes in Computational Science and Engineering, vol.17, 2001.
DOI : 10.1007/978-3-642-56767-4

F. S. Zaitsev, A. G. Shishkin, D. P. Kostomarov, M. R. O-'brien, R. J. Akers et al., The numerical solution of the self-consistent evolution of plasma equilibria, Computer Physics Communications, vol.157, issue.2, pp.107-120, 2004.
DOI : 10.1016/S0010-4655(03)00495-8