메뉴 건너뛰기




Volumn 44, Issue 5, 2006, Pages 1877-1902

Spherical interface dynamos: Mathematical theory, finite element approximation, and application

Author keywords

Finite element analysis; Spherical interface dynamo; Well posedness

Indexed keywords

APPROXIMATION THEORY; ASTROPHYSICS; COMPUTER SIMULATION; FINITE ELEMENT METHOD; GEOMETRY; MEAN FIELD THEORY; STARS;

EID: 33751550813     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/050635596     Document Type: Article
Times cited : (19)

References (36)
  • 1
    • 1542418050 scopus 로고
    • Jupiter's main magnetic field measured by Pioneer 11
    • M. H. ACUNA AND N. F. NESS, Jupiter's main magnetic field measured by Pioneer 11, Nature, 253 (1975), pp. 327-328.
    • (1975) Nature , vol.253 , pp. 327-328
    • ACUNA, M.H.1    NESS, N.F.2
  • 2
    • 0000171411 scopus 로고
    • On a finite element method for solving the three-dimensional Maxwell equations
    • F. ASSOUS, P. DEGOND, E. HEINTZÉ, P. A. RAVIART, AND J. SEGRÉ, On a finite element method for solving the three-dimensional Maxwell equations, J. Comput. Phys., 109 (1993), pp. 222-237.
    • (1993) J. Comput. Phys , vol.109 , pp. 222-237
    • ASSOUS, F.1    DEGOND, P.2    HEINTZÉ, E.3    RAVIART, P.A.4    SEGRÉ, J.5
  • 3
    • 22144490547 scopus 로고    scopus 로고
    • The case for a distributed solar dynamo shaped by near-surface shear
    • A. BRANDENBURG, The case for a distributed solar dynamo shaped by near-surface shear, Astrophy. J., 625 (2005), pp. 539-547.
    • (2005) Astrophy. J , vol.625 , pp. 539-547
    • BRANDENBURG, A.1
  • 4
    • 24744453972 scopus 로고    scopus 로고
    • Astrophyiscal magnetic fields and nonlinear dynamo theory
    • A. BRANDENBURG AND K. SUBRAMANIAN, Astrophyiscal magnetic fields and nonlinear dynamo theory, Physics Reports, 417 (2005), pp. 1-209.
    • (2005) Physics Reports , vol.417 , pp. 1-209
    • BRANDENBURG, A.1    SUBRAMANIAN, K.2
  • 5
    • 0032594393 scopus 로고    scopus 로고
    • Regularity and approximation of systems arising in electromagnetic interrogation of dielectric material
    • H. T. BANKS AND J. ZOU, Regularity and approximation of systems arising in electromagnetic interrogation of dielectric material, Numer. Funct. Anal. Optim., 20 (1999), pp. 609-627.
    • (1999) Numer. Funct. Anal. Optim , vol.20 , pp. 609-627
    • BANKS, H.T.1    ZOU, J.2
  • 7
    • 0001375626 scopus 로고    scopus 로고
    • Turbulent convection under the influence of rotation: Sustaining a strong differential rotation
    • A. S. BRUN AND J. TOOMRE, Turbulent convection under the influence of rotation: sustaining a strong differential rotation, Astrophy. J., 570 (2002), pp. 865-885.
    • (2002) Astrophy. J , vol.570 , pp. 865-885
    • BRUN, A.S.1    TOOMRE, J.2
  • 8
    • 0000602412 scopus 로고
    • Observations of a variable radio source associated with the planet Jupiter
    • B. F. BURKE AND K. L. FRANKLIN, Observations of a variable radio source associated with the planet Jupiter, J. Geophys. Res., 60 (1952), pp. 213-217.
    • (1952) J. Geophys. Res , vol.60 , pp. 213-217
    • BURKE, B.F.1    FRANKLIN, K.L.2
  • 9
    • 0001555745 scopus 로고    scopus 로고
    • Nonlinear saturation of the turbulent alpha effect where a large scale field is imposed
    • F. CATTANEO AND D. W. HUGHES, Nonlinear saturation of the turbulent alpha effect where a large scale field is imposed, Phys. Rev. E, 54 (1996), pp. R4532-R4535.
    • (1996) Phys. Rev. E , vol.54
    • CATTANEO, F.1    HUGHES, D.W.2
  • 10
    • 35548951925 scopus 로고    scopus 로고
    • Spherical Interface Dynamos: Mathematical Theory, Finite Element Approximation and Application
    • Technical Report CUHK-2005-10 331, Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, available online at
    • K. H. CHAN, K. ZHANG, AND J. ZOU, Spherical Interface Dynamos: Mathematical Theory, Finite Element Approximation and Application, Technical Report CUHK-2005-10 (331), Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, 2005, available online at http://www.math.cuhk.edu.hk/en/report/index.php.
    • (2005)
    • CHAN, K.H.1    ZHANG, K.2    ZOU, J.3
  • 11
    • 0035686934 scopus 로고    scopus 로고
    • A nonlinear 3-D spherical alpha-square dynamo using afinitì element method
    • K. H. CHAN, K. ZHANG, J. ZOU, AND G. SCHUBERT, A nonlinear 3-D spherical alpha-square dynamo using afinitì element method, Phys. Earth Planet. Int., 128 (2001), pp. 35-50.
    • (2001) Phys. Earth Planet. Int , vol.128 , pp. 35-50
    • CHAN, K.H.1    ZHANG, K.2    ZOU, J.3    SCHUBERT, G.4
  • 12
    • 0000713960 scopus 로고    scopus 로고
    • Finite element methods with matching and nonmatching meshes for Maxwell equations with discontinuous coefficients
    • Z. CHEN, Q. DU, AND J. ZOU, Finite element methods with matching and nonmatching meshes for Maxwell equations with discontinuous coefficients, SIAM J. Numer. Anal., 37 (2000), pp. 1542-1570.
    • (2000) SIAM J. Numer. Anal , vol.37 , pp. 1542-1570
    • CHEN, Z.1    DU, Q.2    ZOU, J.3
  • 13
    • 0031526610 scopus 로고    scopus 로고
    • P. CIARLET, JR., AND J. ZOU, Finite element convergence for the Darwin model to Maxwell's equations, RAIRO Math. Model. Numer. Anal., 31 (1997), pp. 213-249.
    • P. CIARLET, JR., AND J. ZOU, Finite element convergence for the Darwin model to Maxwell's equations, RAIRO Math. Model. Numer. Anal., 31 (1997), pp. 213-249.
  • 14
    • 0040843328 scopus 로고    scopus 로고
    • P. CIARLET, JR., AND J. ZOU, Fully discrete finite element approaches for time-dependent Maxwell's equations, Numer. Math., 82 (1999), pp. 193-219.
    • P. CIARLET, JR., AND J. ZOU, Fully discrete finite element approaches for time-dependent Maxwell's equations, Numer. Math., 82 (1999), pp. 193-219.
  • 16
    • 0033542250 scopus 로고    scopus 로고
    • A Babcock-Leighton flux transport dynamo with solar-like differential rotation
    • M. DIKPATI AND P. CHARBONNEAU, A Babcock-Leighton flux transport dynamo with solar-like differential rotation, Astrophy. J., 518 (1999), pp. 508-520.
    • (1999) Astrophy. J , vol.518 , pp. 508-520
    • DIKPATI, M.1    CHARBONNEAU, P.2
  • 17
    • 0038415692 scopus 로고
    • Finite element solution of nonlinear elliptic problems
    • M. FEISTAUER AND A. ZENISEK, Finite element solution of nonlinear elliptic problems, Numer. Math., 50 (1987), pp. 451-475.
    • (1987) Numer. Math , vol.50 , pp. 451-475
    • FEISTAUER, M.1    ZENISEK, A.2
  • 19
    • 0029480581 scopus 로고
    • A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle
    • G. GLATZMAIER AND P. ROBERTS, A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle, Phys. Earth Planet. Int., 91 (1995), pp. 63-75.
    • (1995) Phys. Earth Planet. Int , vol.91 , pp. 63-75
    • GLATZMAIER, G.1    ROBERTS, P.2
  • 20
    • 0016333399 scopus 로고
    • Navier-Stokes equations using mixed interpolation
    • J. Oden, ed, UAH Press, Huntsville, AL
    • P. HOOD AND G. TAYLOR, Navier-Stokes equations using mixed interpolation, in Finite Element Methods in Flow Problems, J. Oden, ed., UAH Press, Huntsville, AL, 1974.
    • (1974) Finite Element Methods in Flow Problems
    • HOOD, P.1    TAYLOR, G.2
  • 21
    • 0033211216 scopus 로고    scopus 로고
    • Solar interface dynamo models with a realistic rotation profile
    • J. A. MARKIEL AND J. H. THOMAS, Solar interface dynamo models with a realistic rotation profile, Astrophy. J., 523 (1999), pp. 827-837.
    • (1999) Astrophy. J , vol.523 , pp. 827-837
    • MARKIEL, J.A.1    THOMAS, J.H.2
  • 25
    • 12044253963 scopus 로고
    • A solar dynamo surface wave at the interface between convection and nonuniform rotation
    • E. N. PARKER, A solar dynamo surface wave at the interface between convection and nonuniform rotation, Astrophy. J., 408 (1993), pp. 707-719.
    • (1993) Astrophy. J , vol.408 , pp. 707-719
    • PARKER, E.N.1
  • 27
    • 0001604656 scopus 로고
    • A solar dynamo in the overshoot layer: Cycle period and butterfly diagram
    • G. RUEDIGER AND A. BRANDENBURG, A solar dynamo in the overshoot layer: Cycle period and butterfly diagram, Astronomy and Astrophysics, 296 (1995), pp. 557-566.
    • (1995) Astronomy and Astrophysics , vol.296 , pp. 557-566
    • RUEDIGER, G.1    BRANDENBURG, A.2
  • 28
    • 22444451863 scopus 로고    scopus 로고
    • Helioseismic studies of differential rotation in the solar envelope by the solar oscillations investigation using Michelson Doppler Imager
    • J. SCHOU ET AL., Helioseismic studies of differential rotation in the solar envelope by the solar oscillations investigation using Michelson Doppler Imager, Astrophy. J, 505 (1998), pp. 390-417.
    • (1998) Astrophy. J , vol.505 , pp. 390-417
    • SCHOU ET AL, J.1
  • 29
    • 84966200902 scopus 로고
    • Finite element interpolation of nonsmooth functions satisfying boundary conditions
    • L. R. SCOTT AND S. ZHANG, Finite element interpolation of nonsmooth functions satisfying boundary conditions, Math. Comp., 54 (1990), pp. 483-493.
    • (1990) Math. Comp , vol.54 , pp. 483-493
    • SCOTT, L.R.1    ZHANG, S.2
  • 31
    • 35548968532 scopus 로고    scopus 로고
    • M. STIX, The Sun: An Introduction, Springer-Verlag, Berlin, 2002.
    • M. STIX, The Sun: An Introduction, Springer-Verlag, Berlin, 2002.
  • 33
    • 0002682177 scopus 로고
    • Error estimates for a mixed finite element approximation of the Stokes equations
    • R. VERFÜRTH, Error estimates for a mixed finite element approximation of the Stokes equations, RAIRO Model. Math. Numer. Anal., 18 (1984), pp. 175-182.
    • (1984) RAIRO Model. Math. Numer. Anal , vol.18 , pp. 175-182
    • VERFÜRTH, R.1
  • 34
    • 35548940437 scopus 로고    scopus 로고
    • N. O. WEISS, in Lectures on Solar and Planetary Dynamos, M. R. E. Proctor and A. D. Gilbert, eds., Cambridge University Press, England, 1994.
    • N. O. WEISS, in Lectures on Solar and Planetary Dynamos, M. R. E. Proctor and A. D. Gilbert, eds., Cambridge University Press, England, 1994.
  • 35
    • 84963144974 scopus 로고
    • Convection driven magnetohydrodynamic dynamos in rotating spherical shells
    • K. ZHANG AND F. BUSSE, Convection driven magnetohydrodynamic dynamos in rotating spherical shells, Geophys. Astrophys. Fluid Dyn., 49 (1989), pp. 97-116.
    • (1989) Geophys. Astrophys. Fluid Dyn , vol.49 , pp. 97-116
    • ZHANG, K.1    BUSSE, F.2
  • 36
    • 0034353773 scopus 로고    scopus 로고
    • Magnetohydrodynamics in rapidly rotating spherical systems
    • Annual Reviews, Palo Alto, CA
    • K. ZHANG AND G. SCHUBERT, Magnetohydrodynamics in rapidly rotating spherical systems, in Annual Review of Fluid Mechanics, Vol. 32, Annual Reviews, Palo Alto, CA, 2000, pp. 411-445.
    • (2000) Annual Review of Fluid Mechanics , vol.32 , pp. 411-445
    • ZHANG, K.1    SCHUBERT, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.