References
- Bossavit , A . 1988 . A rationale for edge-elements in 3-D fields computations . IEEE Trans. Magn. , 24 : 74 – 79 .
- Bossavit , A . 1990 . Solving Maxwell's equations in a closed cavity, and the question of spurious modes . IEEE Trans. Magn. , 26 : 702 – 705 .
- Busse , FH . 2002 . Convective flows in rapidly rotating spheres and their dynamo action . Phys. Fluids , 14 : 1301 – 1314 .
- Cébron , D , Le Bars , M , Leontini , J , Maubert , P and Le Gal , P . 2010a . A systematic numerical study of the elliptical instability in a rotating triaxial ellipsoid . Phys. Earth Planet. Int. , 182 : 119 – 128 .
- Cébron , D , Le Bars , M and Meunier , M . 2010c . Tilt-over mode in a precessing triaxial ellipsoid . Phys. Fluids , 22 : 116601
- Cébron , D , Le Bars , M , Moutou , C , Maubert , P and Le Gal , P . 2012a . Elliptical instability in terrestrial planets & moons. , In review for A & A
- D. Cébron, Le Bars, M., Noir, J., Aurnou, J.M., 2012b. Libration driven elliptical instability. Submitted to Phys. Fluids
- Cébron , D , Maubert , P and Le Bars , M . 2010b . Tidal instability in a rotating and differentially heated ellipsoidal shell . Geophys. J. Int. , 182 : 1311 – 1318 .
- Chan , KH , Zhang , K , Zou , J and Schubert , G . 2001 . A non-linear, 3-D spherical α2 dynamo using a finite element method . Phys. Earth Planet. Int. , 128 : 35 – 50 .
- Costabel , M . 1991 . A coercive bilinear form for Maxwell's equations . J. Math. Anal. Appl. , 157 : 527 – 541 .
- Clune , TC , Elliot , JR , Miesch , M , Toomre , J and Glatzmaier , GA . 1999 . Computational aspects of a code to study rotating turbulent convection in spherical shells . Parallel Comput. , 25 : 361 – 380 .
- Christensen , UR , Aubert , J , Cardin , P , Dormy , E , Gibbons , S , Glatzmaier , GA , Grote , E , Honkura , Y , Jones , C , Kono , M and others . 2001 . A numerical dynamo benchmark . Phys. Earth Planet. Int. , 128 : 25 – 34 .
- Donati , JF , Moutou , C , Farès , R , Bohlender , D , Catala , C , Deleuil , M , Shkolnik , E , Cameron , AC , Jardine , MM and Walker , GAH . 2008 . Magnetic cycles of the planet-hosting star τ Bootis . MNRAS , 385 : 1179 – 1185 .
- Dormy , E , Valet , JP and Courtillot , V . 2000 . Numerical models of the geodynamo and observational constraints . Geochem. Geophys. Geosyst , 1 : 1037
- Fares , R , Donati , JF , Moutou , C , Bohlender , D , Catala , C , Deleuil , M , Shkolnik , E , Cameron , AC , Jardine , MM and Walker , GAH . 2009 . Magnetic cycles of the planet-hosting star τ Bootis–II. A second magnetic polarity reversal . MNRAS , 398 : 1383 – 1391 .
- Fournier , A , Bunge , H-P , Hollerbach , R and Vilotte , J-P . 2004 . Application of the spectral-element method to the axisymmetric Navier-Stokes equation . Geophys. J. Int. , 156 : 682 – 700 .
- Fournier , A , Bunge , H-P , Hollerbach , R and Vilotte , J-P . 2005 . A Fourier-spectral element algorithm for thermal convection in rotating axisymmetric containers . J. Comput. Phys. , 204 : 462 – 489 .
- Giesecke , A , Stefani , F and Gerbeth , G . 2008 . Kinematic simulation of dynamo action by a hybrid boundary-element/finite-volume method . Magnetohydrodynamics , 44 : 237 – 252 .
- Gissinger , CJP . 2009 . A numerical model of the VKS experiment . EPL , 87 : 39002
- Glatzmaier , GA and Roberts , PH . 1995 . A three-dimensional self-consistent computer simulation of a geomagnetic field reversal . Nature , 377 : 203 – 209 .
- Greenspan , HP . 1968 . The Theory of Rotating Fluids , Cambridge : Cambridge University Press .
- Guermond , JL , Laguerre , R , Léorat , J and Nore , C . 2007 . An interior penalty Galerkin method for the MHD equations in heterogeneous domains . J. Comput. Phys. , 221 : 349 – 369 .
- Harder , H and Hansen , U . 2005 . A finite-volume solution method for thermal convection and dynamo problems in spherical shells . Geophys. J. Int. , 161 : 522 – 532 .
- Hejda , P and Reshetnyak , M . 2003 . Control volume method for the dynamo problem in the sphere with the free rotating inner Core . Stud. Geophys. Geod. , 47 : 147 – 159 .
- Hejda , P and Reshetnyak , M . 2004 . Control volume method for thermal convection problem in a rotating spherical shell: test on the benchmark solution, Stud . Geophys. Geod. , 48 : 741 – 746 .
- Herreman , W , Le Bars , M and Le Gal , P . 2009 . On the effects of an imposed magnetic field on the elliptical instability in rotating spheroids . Phys. Fluids , 21 : 046602
- Hesthaven , JS and Warburton , T . 2004 . High-order nodal discontinuous Galerkin methods for the Maxwell eigenvalue problem . Phil. Trans. Roy. Soc. London. Ser. A Math. Phys. Eng. Sci. , 362 : 493
- Hindmarsh , AC , Brown , PN , Grant , KE , Lee , SL , Serban , R , Shumaker , DE and Woodward , CS . 2005 . SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers . ACM T. Math. Software , 31 : 363
- Iskakov , AB , Descombes , S and Dormy , EM . 2004 . An integro-differential formulation for magnetic induction in bounded domains: boundary element-finite volume method . J. Comput. Phys. , 197 : 540 – 554 .
- Jiang , BN , Wu , J and Povinelli , LA . 1996 . The origin of spurious solutions in computational electromagnetics . J. Comput. Phys. , 125 : 104 – 123 .
- Jin , JM . 1993 . The Finite Element Method in Electromagnetics , New York : Wiley .
- Jones , CA . 2003 . Dynamos in planets . Stellar Astrophys. Fluid Dyn. , 1 : 159 – 176 .
- Jones , CA . 2011 . Planetary and stellar magnetic fields and fluid dynamos . Annu. Rev. Fluid Mech. , 43 : 1
- Kageyama , A and Sato , T . 1997 . Velocity and magnetic field structures in a magnetohydrodynamic dynamo . Phys. Plasma , 4 : 1569 – 1575 .
- Kaiser , R and Tilgner , A . 1999 . Kinematic dynamos surrounded by a stationary conductor . Phys. Rev. E , 60 : 2949
- Kerswell , RR . 1996 . Upper bounds on the energy dissipation in turbulent precession . J. Fluid Mech. , 321 : 335 – 370 .
- Kerswell , RR . 2002 . Elliptical instability . Annu. Rev. Fluid Mech., , 34 : 83 – 113 .
- Kerswell , RR and Malkus , WVR . 1998 . Tidal instability as the source for Io's magnetic signature . Geophys. Res. Lett. , 25 : 603 – 6 .
- Lacaze , L , Herreman , W , Le Bars , M , Le Dizès , S and Le Gal , P . 2006 . Magnetic field induced by elliptical instability in a rotating spheroid . Geophys. Astrophys. Fluid Dyn. , 100 : 299 – 317 .
- Lacaze , L , Le Gal , P and Le Dizès , S . 2004 . Elliptical instability in a rotating spheroid . J. Fluid Mech. , 505 : 1 – 22 .
- Laguerre , R . Approximation des équations 3D de la magnétohydrodynamique par une méthode spectrale-éléments finis nodaux. C. R. Rencontres Nonlinéaires. 2006
- Loper , DE . 1975 . Torque balance and energy budget for the precessionally driven dynamo . Phys. Earth. Planet. Inter. , 11 : 43 – 60 .
- Malkus , WVR . 1968 . Precession of the earth as the cause of geomagnetism . Science , 160 : 259 – 264 .
- Nédélec , JC . 1980 . Mixed finite elements in R3 . Numer. Math. , 35 : 315 – 341 .
- Nédélec , JC . 1986 . A new family of mixed finite elements in R3 . Numer. Math. , 50 : 57 – 81 .
- Manglik , A , Wicht , J and Christensen , UR . 2010 . A dynamo model with double diffusive convection for Mercury's core . Earth Planet. Sci. Lett. , 289 : 619 – 628 .
- Matsui , H and Okuda , H . 2004 . Development of a simulation code for MHD dynamo processes using the GeoFEM platform . Int. J. Comput. Fluid. Dyn. , 18 : 323 – 332 .
- Matsui , H and Okuda , H . 2005 . MHD dynamo simulation using the GeoFEM platform – verification by the dynamo benchmark test . Int. J. Comput. Fluid Dyn. , 19 : 15 – 22 .
- Monk , P . 2003 . Finite Element Methods for Maxwell's Equations , Oxford : Oxford University Press .
- Paulsen , KD and Lynch , DR . 1991 . Elimination of vector parasites in finite element Maxwell solutions . IEEE Trans. Microwave Theo. Tech. , 39 : 395 – 404 .
- Ponomarenko , YB . 1973 . Theory of the hydromagnetic generator . J. Appl. Mech. Tech. Phys. , 14 : 775 – 778 .
- Rieutord , M . 2008 . The solar dynamo . C. R. , 9 : 757 – 765 .
- Rochester , MG , Jacobs , JA , Smylie , DE and Chong , KF . 1975 . Can precession power the geomagnetic dynamo? . Geophys. J. R. Astron. Soc. , 43 : 661 – 678 .
- Sun , D , Manges , J , Yuan , X and Cendes , Z . 1995 . Spurious modes in finite-element methods . Antennas Propagation Mag. IEEE , 37 : 12 – 24 .
- Thess , A and Zikanov , O . 2007 . Transition from two-dimensional to three-dimensional magnetohydrodynamic turbulence . J. Fluid Mech. , 579 : 383 – 412 .
- Tilgner , A . 1998 . On models of precession driven core flow . Stud. Geophys. Geod. , 42 : 232 – 238 .
- Tilgner , A . 2005 . Precession driven dynamos . Phys. Fluids , 17 : 034104
- Volakis , JL , Chatterjee , A and Kempel , L . 1998 . Finite Element Methods for Electromagnetics: Antennas, Microwave Circuits and Scattering Applications , New York : IEEE Press .
- Wicht , J and Tilgner , A . 2010 . Theory and modeling of planetary dynamos . Space Sci. Rev. , 152 : 501 – 542 .
- Wu , CC and Roberts , PH . 2009 . On a dynamo driven by topographic precession . Geophys. Astrophys. Fluid Dyn. , 103 : 467 – 501 .