V. Taylor-couette-ow and .. , The angular velocity of the lids and the inner cylinder is ? i = 1; the outer cylinder is motionless. A radial jet ows inward at the equator. Represented are the poloidal ow (vectors and streamlines) ?0.2 ? V r ? 0.3, and ?0, and the toroidal (or azimuthal), p.202

F. Taylor-couette-ow, V. I. , ?. =. , and .. , R e = 120, and A = 2.5. The lids and the inner cylinder rotate with angular speed ? i = 0.55; the outer cylinder is motionless. A radial jet ows inwards at the equator. Represented are the poloidal ow (vectors and streamlines, ?0.7 ? V r ? 1.4, ?1.1 ? V z ? 1.1, and the toroidal, p.204

R. Kinematic-dynamo, =. , and .. , Growthrate of Fourier mode m = 1 for the modied Taylor- Couette ow, V ? , as a function of ? for R m = 100 and R m = 200, p.205

. Kinematic, Magnetic eigenvector for Fourier mode m = 1 Represented in (a) to (f) are the radial, azimuthal, and vertical components, normalized by the square root of the magnetic energy, in two complementary planes, with 0 ? r ? 2, ?1 ? z ? 1 (the z?axis is on the left): for ? = 0

V. Kinematic-dynamo-of-ow, Growthrate of the Fourier mode m = 1 as a function of R m, p.207

R. Kinematic-dynamo-with-v-i-ow, =. , and .. , Growthrate of the Fourier mode m = 1 as a function of R m . ROT: rotating inner core; NO-ROT: non-rotating inner core (but inner wall rotates), p.207

V. Kinematic-dynamo-with-ow, R. , and =. , Magnetic eigenvector for Fourier mode m = 1 Represented in (a) to (f) are the radial, azimuthal, and vertical components, normalized by the square root of the magnetic energy, in two complementary planes: for ? = 0, ?0.9 ? H r ? 0.2 (every 0.1), ?1.4 ? H ? ? 0.35 (every 0.25) and ?0.6 ? H z ? 0.6 (every 0.1); for ? = ?, p.208

K. For-dierent-reynolds-numbers, R. , and ?. , 223 G.5 (Color online) Time evolution of the asymmetry ratio r a for dierent Reynolds numbers R e ? [700 224 G.6 (Color online) Time evolution of the asymmetry ratio r a at R e = 750 and R e = 800 to show the short period of oscillations (Color online) Time evolution of the magnetic energy M in the conducting uid (a) in the linear regime from t = 192 at R e = 1200 and various R m as indicated (in lin-log scale) and (b) in the nonlinear regime from t = 192 to t = 287, p.226, 1200.

E. Vantieghem and S. Zurich, with the Poincaré solution as initial data: (a) solution with the SFEMaNS code and (b) solution with a Finite Volume code (courtesy of S, p.256

M. Taylor-couette-ow and .. , normalization factor ?(?), poloidal to toroidal ratio ?(?) and maximum of the velocity modulus V max, p.203

]. J. Bibliographie1, K. A. Abshagen, J. Clie, T. Langenberg, G. Mullin et al., Taylor Couette ow with independently rotating end plates. Theoretical and Computational Fluid Dynamics, pp.129136-00162, 1007.

A. Robert, J. J. Adams, and . Fournier, Sobolev spaces, 2003.

A. Alonso, A mathematical justication of the low-frequency heterogeneous timeharmonic Maxwell equations, Math. Models Methods Appl. Sci, vol.9, issue.3, p.475489, 1999.

P. R. Amestoy, I. S. Du, J. Koster, and J. Excellent, A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling, SIAM Journal on Matrix Analysis and Applications, vol.23, issue.1, p.1541, 2001.
DOI : 10.1137/S0895479899358194

URL : https://hal.archives-ouvertes.fr/hal-00808293

P. R. Amestoy, A. Guermouche, J. Excellent, and S. Pralet, Hybrid scheduling for the parallel solution of linear systems, Parallel Computing, vol.32, issue.2, p.136156, 2006.
DOI : 10.1016/j.parco.2005.07.004

URL : https://hal.archives-ouvertes.fr/hal-00358623

P. R. Amestoy, MUMPS : a MUltifrontal Massively Parallel sparse direct Solver

D. N. Arnold, An interior penalty nite element method with discontinuous elements, SIAM J. Numer. Anal, vol.19, p.742760, 1982.

R. Avalos-zuñiga and F. Plunian, Inuence of inner and outer walls electromagnetic properties on the onset of a stationary dynamo action, Eur. Phys. J. B, vol.47, p.127135, 2005.

R. Avalos-zuñiga, F. Plunian, and A. Gailitis, Influence of electromagnetic boundary conditions onto the onset of dynamo action in laboratory experiments, Physical Review E, vol.68, issue.6, p.66307, 2003.
DOI : 10.1103/PhysRevE.68.066307

I. Babu²ka and J. Osborn, Eigenvalue problems In Finite Element Methods (Part 1), volume 2 of Handbook of Numerical Analysis, pp.641-787, 1991.

G. A. Baker, Finite element methods for elliptic equations using nonconforming elements, Mathematics of Computation, vol.31, issue.137, p.4559, 1977.
DOI : 10.1090/S0025-5718-1977-0431742-5

S. Balay, J. Brown, K. Buschelman, V. Eijkhout, W. D. Gropp et al., PETSc users manual, 2012.

S. Balay, W. D. Gropp, L. C. Mcinnes, and B. F. Smith, Ecient management of parallelism in object oriented numerical software libraries, Modern Software Tools in Scientic Computing, p.163202, 1997.

R. A. Bayliss, C. B. Forest, M. D. Nornberg, E. J. Spence, and P. W. Terry, Numerical simulations of current generation and dynamo excitation in a mechanically forced turbulent ow, Phys. Rev. E, pp.75-026303, 2007.

C. Bernardi, Optimal nite element interpolation on curved domains, SIAM J. Numer. Anal, vol.26, p.12121240, 1989.
DOI : 10.1137/0726068

A. Bonito and J. Guermond, Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange nite elements, Math. Comp, vol.80, issue.276, p.18871910, 2011.

A. Bonito, J. Guermond, and F. Luddens, Note on the regularity of the Maxwell equations in heterogeneous media. submitted, 2012.

A. Bossavit, Computational Electromagnetism, Variational Formulations, Complementary , Edge Elements, volume 2 of Electromagnetism, 1998.

M. Bourgoin, F. Pétrélis, C. Gasquet, A. Guigon, J. Luciani et al., Magnetohydrodynamics measurements in the von K??rm??n sodium experiment, Physics of Fluids, vol.14, issue.9, p.30463058, 2002.
DOI : 10.1063/1.1497376

J. H. Bramble, T. V. Kolev, and J. E. Pasciak, The approximation of the Maxwell eigenvalue problem using a least-squares method, Mathematics of Computation, vol.74, issue.252, p.15751598, 2005.
DOI : 10.1090/S0025-5718-05-01759-X

J. H. Bramble and J. E. Pasciak, A new approximation technique for div-curl systems, Mathematics of Computation, vol.73, issue.248, p.17391762, 2004.
DOI : 10.1090/S0025-5718-03-01616-8

H. Brezis, Analyse fonctionnelle Théorie et applications. [Functional Analysis, Theory and applications]. Applied Mathematics Series for the Master's Degree. Masson, 1983.

A. Bua, P. C. Jr, and E. Jamelot, Solving electromagnetic eigenvalue problems in polyhedral domains with nodal nite elements, Numer. Math, vol.113, p.497518, 2009.

A. Bua and I. Perugia, Discontinuous Galerkin approximation of the Maxwell eigenproblem, SIAM J. Numer. Anal, vol.44, issue.5, p.21982226, 2006.

E. Bullard, The magnetic eld within the Earth, Proc. Roy. Soc. Lond. A, vol.197, p.433453, 1051.

E. Bullard, The stability of a homopolar dynamo, Mathematical Proceedings of the Cambridge Philosophical Society, vol.42, issue.04, p.744760, 1955.
DOI : 10.1098/rsta.1954.0018

F. H. Busse and J. Wicht, A simple dynamo caused by conductivity variations, Geophysical & Astrophysical Fluid Dynamics, vol.168, issue.1-4, p.135144, 1992.
DOI : 10.1016/0012-821X(89)90154-4

P. Cardin, E. Dormy, and D. Jault, MHD ow in a slightly dierentially rotating spherical shell, with conducting inner core, in a dipolar magnetic eld, Earth and Planetary Science Letters, vol.160, p.1530, 1998.

J. E. Channell, D. A. Hodell, J. Mcmanus, and B. Lehman, Orbital modulation of the Earth's magnetic eld intensity, Nature, vol.394, p.464468, 1998.

U. R. Christensen, J. Aubert, P. Cardin, E. Dormy, S. Gibbons et al., A numerical dynamo benchmark Dynamics and Magnetic Fields of the Earth's and Planetary Interiors, Physics of the Earth and Planetary Interiors, vol.128, pp.1-425, 2001.

P. , C. Jr, F. Lefèvre, S. Lohrengel, and S. Nicaise, Weighted regularization for composite materials in electromagnetism, Modélisation Mathématique et Analyse Numérique, vol.44, p.75108, 2010.

P. Clément, Approximation by nite element functions using local regularization, RAIRO, Anal. Num, vol.9, p.7784, 1975.

S. A. Colgate, H. Beckley, J. Si, J. Martinic, D. Westpfahl et al., Dynamo, Physical Review Letters, vol.106, issue.17, p.175003, 2011.
DOI : 10.1103/PhysRevLett.106.175003

M. Costabel and M. Dauge, Weighted regularization of Maxwell equations in polyhedral domains, Numerische Mathematik, vol.93, issue.2, p.239278, 2002.
DOI : 10.1007/s002110100388

M. Costabel, M. Dauge, and S. Nicaise, Singularities of Maxwell interface problems, ESAIM: Mathematical Modelling and Numerical Analysis, vol.33, issue.3, p.627649, 1999.
DOI : 10.1051/m2an:1999155

T. G. Cowling, The magnetic eld of sunspots, Mon. Not. Roy. Astr. Soc, vol.94, p.3948, 1934.

M. Dauge, Benchmark for Maxwell, 2009.

R. Dautray and J. Lions, Mathematical Analysis and Numerical Methods for Functional and variational methods, Science and Technology, vol.2, 1988.

L. Desvillettes and C. Villani, On a variant of Korn's inequality arising in statistical mechanics, ESAIM: Control, Optimisation and Calculus of Variations, vol.8, p.603619, 2002.
DOI : 10.1051/cocv:2002036

W. Dobler, P. Frick, and R. Stepanov, Screw dynamo in a time-dependent pipe flow, Physical Review E, vol.67, issue.5, p.56309, 2003.
DOI : 10.1103/PhysRevE.67.056309

M. L. Dudley and R. W. James, Time-dependent kinematic dynamos with stationary ows, Proc. Roy. Soc. London A, p.407429, 1989.
DOI : 10.1098/rspa.1989.0112

G. Duvaut and J. Lions, Les inéquations en mécanique et en physique, 1972.

A. Ern and J. Guermond, Elements nis : Théorie, applications, mise en ÷uvre, of SMAI Series on Mathematics and Applications, 2002.

A. Ern and J. Guermond, Theory and practice of nite elements, Applied Mathematical Sciences, vol.159, 2004.

M. Fortin, An analysis of the convergence of mixed nite element methods, RAIRO, Anal. Num, vol.11, p.341354, 1977.

P. Frick, S. Khripchenko, S. Denisov, D. Sokolo, and J. Pinton, Eective magnetic permeability of a turbulent uid with macroferroparticles, Eur. Phys. J. B, vol.25, p.399402, 2002.

A. Gailitis, O. Lielausis, S. Dement-'ev, E. Platacis, and A. Cifersons, Detection of a Flow Induced Magnetic Field Eigenmode in the Riga Dynamo Facility, Physical Review Letters, vol.84, issue.19, p.4365, 2000.
DOI : 10.1103/PhysRevLett.84.4365

A. Gailitis, O. Lielausis, E. Platacis, G. Gerbeth, and F. Stefani, Riga dynamo experiment and its theoretical background, Physics of Plasmas, vol.11, issue.5, p.28382843, 2004.
DOI : 10.1063/1.1666361

B. Gallet, F. Pétrélis, and S. Fauve, Dynamo action due to spatially dependent magnetic permeability, EPL (Europhysics Letters), vol.97, issue.6, p.69001, 2012.
DOI : 10.1209/0295-5075/97/69001

R. F. Gans, On hydromagnetic precession in a cylinder, Journal of Fluid Mechanics, vol.219, issue.01, p.111130, 1970.
DOI : 10.1017/S0022112068001655

A. Giesecke, C. Nore, F. Plunian, R. Laguerre, A. Ribeiro et al., Generation of axisymmetric modes in cylindrical kinematic mean-eld dynamos of VKS type, Geophys. Astrophys. Fluid Dyn, vol.104, issue.2, p.249271, 2010.

A. Giesecke, C. Nore, F. Stefani, G. Gerbeth, J. Léorat et al., Electromagnetic induction in non-uniform domains, Geophysical & Astrophysical Fluid Dynamics, vol.44, issue.5-6, p.505529, 2010.
DOI : 10.1016/S0010-4655(98)00139-8

URL : https://hal.archives-ouvertes.fr/hal-01102082

A. Giesecke, F. Stefani, and G. Gerbeth, Kinematic simulations of dynamo action with a hybrid boundary-element/nite-volume method, Magnetohydrodynamics, vol.44, issue.3, pp.237-252, 2008.

A. Giesecke, F. Stefani, and G. Gerbeth, Role of Soft-Iron Impellers on the Mode Selection in the von K??rm??n???Sodium Dynamo Experiment, Physical Review Letters, vol.104, issue.4, p.44503, 2010.
DOI : 10.1103/PhysRevLett.104.044503

V. Girault and P. Raviart, Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms, 1986.

C. Gissinger, S. Fauve, and E. Dormy, Bypassing Cowling???s Theorem in Axisymmetric Fluid Dynamos, Physical Review Letters, vol.101, issue.14, p.144502, 2008.
DOI : 10.1103/PhysRevLett.101.144502

C. Gissinger, A. Iskakov, S. Fauve, and E. Dormy, Effect of magnetic boundary conditions on the dynamo threshold of von K??rm??n swirling flows, EPL (Europhysics Letters), vol.82, issue.2, p.29001, 2008.
DOI : 10.1209/0295-5075/82/29001

G. A. Glatzmaier and P. H. Roberts, A three-dimensional self-consistent computer simulation of a geomagnetic eld reversal, Nature, vol.377, p.203209, 1995.

P. Grisvard, Elliptic problems in nonsmooth domains, Monographs and Studies in Mathematics, vol.24, 1985.
DOI : 10.1137/1.9781611972030

J. Guermond, The LBB condition in fractional Sobolev spaces and applications, IMA Journal of Numerical Analysis, vol.29, issue.3, 2006.
DOI : 10.1093/imanum/drn028

J. Guermond, R. Laguerre, J. Léorat, and C. Nore, An interior penalty Galerkin method for the MHD equations in heterogeneous domains, Journal of Computational Physics, vol.221, issue.1, pp.349-369, 2007.
DOI : 10.1016/j.jcp.2006.06.045

J. Guermond, R. Laguerre, J. Léorat, and C. Nore, Nonlinear magnetohydrodynamics in axisymmetric heterogeneous domains using a fourier/nite element technique and an interior penalty method, J. Comput. Phys, vol.228, p.27392757, 2009.

J. Guermond, J. Léorat, F. Luddens, C. Nore, and A. Ribeiro, Eects of discontinuous magnetic permeability on magnetodynamic problems, J. Comput. Phys, vol.230, p.62996319, 2011.

E. Haber and U. M. Ascher, Fast Finite Volume Simulation of 3d electromagnetic problems with highly discontinuous coecients, SIAM J. Sci. Comput, vol.22, 2001.

R. Hewitt, S. Mullin, M. A. Tavener, P. Khan, and . Treacher, Nonlinear vortex development in rotating ows, Philosophical Transactions of the Royal Society A : Mathematical, Physical and Engineering Sciences, p.36613171329, 1868.

R. Hide and T. N. Palmer, Generalization of Cowling's theorem, Geophysical & Astrophysical Fluid Dynamics, vol.15, issue.3-4, p.301309, 1982.
DOI : 10.1080/03091928208208961

A. B. Iskakov, S. Descombes, and E. Dormy, An integro-dierential formulation for magnetic induction in bounded domains : boundary element-nite volume method, J. Comput. Phys, vol.197, p.540554, 2004.

A. B. Iskakov and E. Dormy, On magnetic boundary conditions for non-spectral dynamo simulations, Geophysical & Astrophysical Fluid Dynamics, vol.16, issue.6, p.481492, 2005.
DOI : 10.1016/j.jcp.2003.10.034

D. S. Jerison and C. E. Kenig, The Neumann problem on Lipschitz domains, Bulletin of the American Mathematical Society, vol.4, issue.2, p.203207, 1981.
DOI : 10.1090/S0273-0979-1981-14884-9

D. S. Jerison and C. E. Kenig, The Inhomogeneous Dirichlet Problem in Lipschitz Domains, Journal of Functional Analysis, vol.130, issue.1, p.161219, 1995.
DOI : 10.1006/jfan.1995.1067

F. Jochmann, An Hs-Regularity Result for the Gradient of Solutions to Elliptic Equations with Mixed Boundary Conditions, Journal of Mathematical Analysis and Applications, vol.238, issue.2, p.429450, 1999.
DOI : 10.1006/jmaa.1999.6518

C. A. Jones, P. Boronski, A. S. Brun, G. A. Glatzmaier, T. Gastine et al., Anelastic convection-driven dynamo benchmarks, Icarus, vol.216, issue.1, pp.120-135, 2011.
DOI : 10.1016/j.icarus.2011.08.014

URL : http://hdl.handle.net/11858/00-001M-0000-0015-0715-9

A. Kageyama, T. Miyagoshi, and T. Sato, Formation of current coils in geodynamo simulations, Nature, vol.93, issue.7208, p.11061109, 2008.
DOI : 10.1038/nature07227

G. Karypis and V. Kumar, A Fast and Highly Quality Multilevel Scheme for Partitioning Irregular Graphs, SIAM Journal on Scientic Computing, vol.20, issue.1, p.359392, 1999.

S. Kenjere² and K. Hanjali¢, Numerical Simulation of a Turbulent Magnetic Dynamo, Physical Review Letters, vol.98, issue.10
DOI : 10.1103/PhysRevLett.98.104501

F. Krause and K. Radler, Mean-Field Magnetohydrodynamics and Dynamo Theory, 1980.

W. Kuang and J. Bloxham, An Earth-like numerical dynamo model, Nature, vol.389, pp.371-374, 1997.

W. Kuang and J. Bloxham, Numerical Modeling of Magnetohydrodynamic Convection in a Rapidly Rotating Spherical Shell: Weak and Strong Field Dynamo Action, Journal of Computational Physics, vol.153, issue.1, pp.51-81, 1999.
DOI : 10.1006/jcph.1999.6274

R. Lagrange, C. Eloy, F. Nadal, and P. Meunier, Instability of a fluid inside a precessing cylinder, Physics of Fluids, vol.20, issue.8, p.81701, 2008.
DOI : 10.1063/1.2963969.1

URL : https://hal.archives-ouvertes.fr/hal-00326205

R. Laguerre, Approximation des équations de la MHD par une méthode hybride spectraleéléments nis nodaux : application à l'eet dynamo, 2006.

R. Laguerre, C. Nore, A. Ribeiro, J. Léorat, J. Guermond et al., , 104501 (2008)], Physical Review Letters, vol.101, issue.21, p.219902, 2008.
DOI : 10.1103/PhysRevLett.101.219902

R. Laguerre, C. Nore, A. Ribeiro, J. Léorat, J. Guermond et al., Impact of Impellers on the Axisymmetric Magnetic Mode in the VKS2 Dynamo Experiment, Physical Review Letters, vol.101, issue.10, p.104501, 2008.
DOI : 10.1103/PhysRevLett.101.104501

URL : https://hal.archives-ouvertes.fr/hal-00381958

T. Lehner, W. Mouhali, J. Léorat, and A. Mahalov, Mode coupling analysis and dierential rotation in a ow driven by a precessing cylindrical container, Geophys. Astrophys. Fluid Dyn, vol.104, issue.4, p.369401, 2010.

R. B. Lehoucq, D. C. Sorensen, and C. Yang, ARPACK users' guide, volume 6 of Software, Environments and Tools Solution of large-scale eigenvalue problems with implictly restarted Arnoldi methods, Society for Industrial and Applied Mathematics (SIAM), 1998.

J. Léorat, P. Lallemand, J. Guermond, and F. Plunian, Dynamo Action, Between Numerical Experiments and Liquid Sodium Devices, NATO Science Series, II Mathematics Physics and Chemistry, vol.26, p.2533, 2001.
DOI : 10.1007/978-94-010-0788-7_4

J. Léorat and C. Nore, Interplay between experimental and numerical approaches in the uid dynamo problem, Comptes Rendus Physique, vol.9, p.741748, 2008.

J. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, vol.1, 1969.
DOI : 10.1007/bf00249679

J. Lions and J. Peetre, Sur Une Classe D???Espaces D???Interpolation, Publications math??matiques de l'IH??S, vol.XIV, issue.1, p.568, 1964.
DOI : 10.1007/BF02684796

P. W. Livermore and A. Jackson, On magnetic energy instability in spherical stationary ows, Proceedings of the Royal Society of London. Series A : Mathematical, Physical and Engineering Sciences, p.46014531476, 2004.

F. J. Lowes and I. Wilkinson, Geomagnetic Dynamo: A Laboratory Model, Nature, vol.250, issue.4886, p.1158, 1963.
DOI : 10.1038/1981158a0

F. J. Lowes and I. Wilkinson, Geomagnetic Dynamo: An Improved Laboratory Model, Nature, vol.58, issue.5155, p.717, 1968.
DOI : 10.1016/0003-4916(58)90054-X

W. V. Malkus, Precession of the Earth as the Cause of Geomagnetism: Experiments lend support to the proposal that precessional torques drive the earth's dynamo, Science, vol.160, issue.3825, p.160259264, 1968.
DOI : 10.1126/science.160.3825.259

L. Marié, J. Burguete, F. Daviaud, and J. Léorat, Numerical study of homogeneous dynamo based on experimental von Kármán type ows, European Physical Journal B, vol.33, p.469485, 2003.

L. Marié, C. Normand, and F. Daviaud, Galerkin analysis of kinematic dynamos in the von K??rm??n geometry, Physics of Fluids, vol.18, issue.1, p.17102, 2006.
DOI : 10.1063/1.2158267

L. Marié, F. Pétrélis, M. Bourgoin, J. Burguete, A. Chiaudel et al., Open questions about homogeneous uid dynamos : the VKS experiment, Magnetohydrodynamics, vol.38, p.156169, 2002.

F. Marques and J. M. Lopez, Onset of three-dimensional unsteady states in smallaspect-ratio TaylorCouette ow, Journal of Fluid Mechanics, vol.561, p.255277, 2006.

L. , M. Witkowski, P. Marty, and J. S. Walker, Multidomain analytical-numerical solution for a rotating magnetic eld with nite-length conducting cylinder, IEEE Trans. on Magnetics, vol.36, p.452460, 2000.

R. M. Mason and R. R. , Chaotic dynamics in a strained rotating ow : a precessing plane uid layer, J. Fluid Mech, vol.471, p.71106, 2002.

N. G. Meyers, An L p e-estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Scuola Norm. Sup. Pisa, vol.17, issue.3, p.189206, 1963.

H. K. Moatt, Magnetic Field Generation in Electrically Conducting Fluids. Cambridge Monographs on Mechanics and Applied Mathematics, 1978.

R. Monchaux, M. Berhanu, S. Aumaitre, A. Chiaudel, F. Daviaud et al., The von Kármán sodium experiment

R. Monchaux, M. Berhanu, M. Bourgoin, . Ph, M. Odier et al., Generation of a Magnetic Field by Dynamo Action in a Turbulent Flow of Liquid Sodium, Physical Review Letters, vol.98, issue.4, p.44502, 2007.
DOI : 10.1103/PhysRevLett.98.044502

URL : https://hal.archives-ouvertes.fr/hal-00492342

P. Monk, Finite element methods for Maxwell's equations. Numerical Mathematics and Scientic Computation, 2003.

U. Müller, R. Stieglitz, and S. Horanyi, A two-scale hydromagnetic dynamo experiment, Journal of Fluid Mechanics, vol.498, p.3171, 2004.
DOI : 10.1017/S0022112003006700

C. Nore, M. Brachet, H. Politano, and A. Pouquet, Dynamo action in the TaylorGreen vortex near threshold, Phys. Plasmas, p.14, 1997.

C. Nore, J. Léorat, J. Guermond, and F. Luddens, Nonlinear dynamo action in a precessing cylindrical container, Physical Review E, vol.84, issue.1, p.16317, 2011.
DOI : 10.1103/PhysRevE.84.016317

P. Olson, Probing Earth's dynamo, Nature, vol.389, p.337338, 1997.

J. E. Osborn, Spectral approximation for compact operators, Mathematics of Computation, vol.29, issue.131, p.712725, 1975.
DOI : 10.1090/S0025-5718-1975-0383117-3

E. N. Parker, Hydromagnetic Dynamo Models., The Astrophysical Journal, vol.122, p.293, 1955.
DOI : 10.1086/146087

F. Pétrélis, M. Bourgoin, L. Marié, J. Burguete, A. Chiaudel et al., Nonlinear Magnetic Induction by Helical Motion in a Liquid Sodium Turbulent Flow, Physical Review Letters, vol.90, issue.17, p.174501, 2003.
DOI : 10.1103/PhysRevLett.90.174501

F. Pétrélis, N. Mordant, and S. Fauve, On the magnetic elds generated by experimental dynamos, Geophysical & Astrophysical Fluid Dynamics, vol.101, p.289323, 2007.

Y. B. Ponomarenko, Theory of the hydrodynamic generator, J. Appl. Mech. Tech. Phys, vol.14, p.775778, 1973.

Y. Ponty, P. D. Mininni, J. Pinton, H. Politano, and A. Pouquet, Dynamo action at low magnetic Prandtl numbers: mean flow versus fully turbulent motions, New Journal of Physics, vol.9, issue.8, p.296, 2007.
DOI : 10.1088/1367-2630/9/8/296

URL : https://hal.archives-ouvertes.fr/hal-00388153

F. Ravelet, A. Chiaudel, F. Daviaud, and J. Léorat, Toward an experimental von K??rm??n dynamo: Numerical studies for an optimized design, Physics of Fluids, vol.17, issue.11, p.117104, 2005.
DOI : 10.1063/1.2130745

A. Ribeiro, Approche spectrale/éléments nis pour des problèmes de magnétohydrodynamique non-linéaires, 2010.

G. O. Roberts, Dynamo action of uid motions with two-dimensional periodicity, Phil. Trans. Roy. Soc. of London. Series A, vol.271, p.411454, 1972.

P. H. Roberts, An introduction to Magnetohydrodynamics. Longmans, 1967.

P. H. Roberts, G. A. Glatzmaier, and T. L. Clune, Numerical simulation of a spherical dynamo excited by a ow of von Kármán type, Geophysical & Astrophysical Fluid Dynamics, vol.104, p.207220, 2010.

A. Sakuraba and P. H. Roberts, Generation of a strong magnetic eld using uniform heat ux at the surface of the core, Nature Geoscience, vol.2, p.802805, 2009.

G. Savaré, Regularity Results for Elliptic Equations in Lipschitz Domains, Journal of Functional Analysis, vol.152, issue.1, p.176201, 1998.
DOI : 10.1006/jfan.1997.3158

A. Schekochihin, A. Iskakov, S. Cowley, J. Mc-williams, M. Proctor et al., Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers, New Journal of Physics, vol.9, issue.8, p.300, 2007.
DOI : 10.1088/1367-2630/9/8/300

URL : http://doi.org/10.1088/1367-2630/9/8/300

R. L. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions, Mathematics of Computation, vol.54, issue.190, p.483493, 1990.
DOI : 10.1090/S0025-5718-1990-1011446-7

G. Sell, Global attractors for the three-dimensional Navier-Stokes equations, Journal of Dynamics and Differential Equations, vol.8, issue.1, pp.133-143, 1996.
DOI : 10.1007/BF02218613

F. Stefani, S. Eckert, G. Gerbeth, A. Giesecke, . Th et al., DresDyn -A new facility for MHD experiments with liquid sodium, Magnetohydrodynamics, vol.48, p.103113, 2012.

F. Stefani, G. Gerbeth, and A. Gailitis, Velocity prole optimization for the Riga dynamo experiment, Transfer Phenomena in Magnetohydrodynamic and Electroconducting Flows, p.31, 1999.

F. Stefani, A. Giesecke, and G. Gerbeth, Numerical simulations of liquid metal experiments on cosmic magnetic elds, Theor. Comp. Fluid Dyn, vol.23, p.405429, 2009.

F. Stefani, M. Xu, G. Gerbeth, F. Ravelet, A. Chiaudel et al., Ambivalent effects of added layers on steady kinematic dynamos in cylindrical geometry: application to the VKS experiment, European Journal of Mechanics - B/Fluids, vol.25, issue.6, p.894, 2006.
DOI : 10.1016/j.euromechflu.2006.02.002

URL : https://hal.archives-ouvertes.fr/hal-00180228

K. Stewartson and P. H. Roberts, On the motion of liquid in a spheroidal cavity of a precessing rigid body, Journal of Fluid Mechanics, vol.49, issue.01, p.120, 1963.
DOI : 10.1086/147555

R. Stieglitz and U. Müller, Experimental demonstration of a homogeneous two-scale dynamo, Physics of Fluids, vol.13, issue.3, p.561, 2001.
DOI : 10.1063/1.1331315

J. M. Stone and N. M. Zeus-2d, A radiation magnetohydrodynamics code for astrophysical ows in two space dimensions. I -The hydrodynamic algorithms and tests

J. M. Stone and N. M. Zeus-2d, ZEUS-2D: A Radiation Magnetohydrodynamics Code for Astrophysical Flows in Two Space Dimensions. II. The Magnetohydrodynamic Algorithms and Tests, The Astrophysical Journal Supplement Series, vol.80, p.791, 1992.
DOI : 10.1086/191681

K. Subramanian, A. Shukurov, and N. E. Haugen, Evolving turbulence and magnetic fields in galaxy clusters, Monthly Notices of the Royal Astronomical Society, vol.366, issue.4, p.1437, 2006.
DOI : 10.1111/j.1365-2966.2006.09918.x

L. Tartar, An introduction to Sobolev spaces and interpolation spaces, of Lecture Notes of the Unione Matematica Italiana, 2007.

S. J. Tavener, T. Mullin, and K. A. Clie, Novel bifurcation phenomena in a rotating annulus, Journal of Fluid Mechanics, vol.65, issue.-1, p.483497, 1991.
DOI : 10.1017/S0022112074001224

R. Temam, Navier Stokes Equations: Theory and Numerical Analysis, Journal of Applied Mechanics, vol.45, issue.2, 1984.
DOI : 10.1115/1.3424338

A. Tilgner, On models of precession driven core ow. Studia geoph. et geod, 1998.

A. Tilgner, Numerical simulation of the onset of dynamo action in an experimental two-scale dynamo, Physics of Fluids, vol.14, issue.11, p.4091, 2002.
DOI : 10.1063/1.1513156

A. Tilgner, Precession driven dynamos, Physics of Fluids, vol.17, issue.3, p.34104, 2005.
DOI : 10.1063/1.1852576

A. Tilgner, Kinematic dynamos with precession driven ow in a sphere, Geophys. Astrophys. Fluid Dyn, vol.101, issue.11, 2007.

A. Tilgner and F. H. Busse, Simulation of the bifurcation diagram of the Karlsruhe dynamo, Magnetohydrodynamics, vol.38, p.3540, 2002.

S. M. Tobias, Modulation of solar and stellar dynamos, Astronomische Nachrichten, vol.323, issue.3-4, p.417423, 2002.
DOI : 10.1002/1521-3994(200208)323:3/4<417::AID-ASNA417>3.0.CO;2-U

A. De-la-torre and J. Burguete, Slow Dynamics in a Turbulent von K??rm??n Swirling Flow, Physical Review Letters, vol.99, issue.5, p.5401, 2007.
DOI : 10.1103/PhysRevLett.99.054101

G. Verhille, N. Plihon, M. Bourgoin, P. Odier, and J. Pinton, Induction in a von K??rm??n flow driven by ferromagnetic impellers, New Journal of Physics, vol.12, issue.3, p.33006, 2010.
DOI : 10.1088/1367-2630/12/3/033006

J. Wicht and F. H. Busse, Dynamo Action Induced by Lateral Variation of Electrical Conductivity, Solar and Planetary Dynamos, p.329337, 1993.
DOI : 10.1017/CBO9780511662874.044

A. P. Willis and C. F. Barenghi, A Taylor-Couette dynamo, Astronomy and Astrophysics, vol.393, issue.1, p.339343, 2002.
DOI : 10.1051/0004-6361:20021007

C. Wu and P. H. Roberts, On a dynamo driven by topographic precession, Geophysical & Astrophysical Fluid Dynamics, vol.27, issue.6, p.467501, 2009.
DOI : 10.1080/03091920701450333

U. Ziegler, A three-dimensional Cartesian adaptive mesh code for compressible magnetohydrodynamics, Computer Physics Communications, vol.116, issue.1, p.6577, 1999.
DOI : 10.1016/S0010-4655(98)00139-8