The Three Dimensional Non-conforming Finite Element Solution of the Chapman-Ferraro Problem

Journal of Computational Physics

Volumn 150, Issue 2, 1999, Pages 549-560

  Klouček, Petr ^a   Toffoletto, Frank R ^a  

^a RICE UNIVERSITY   (United States)

Author keywords

Chapman Ferraro currents; Laplace's equation; Magnetopause; Magnetosphere; Neumann boundary value problem; Non conforming finite elements

Indexed keywords

FINITE ELEMENT METHOD; LAPLACE TRANSFORMS; MAGNETIC FIELD EFFECTS; MAGNETOPAUSE;

'CURRENT; CHAPMAN-FERRARO CURRENT; FIELD MODEL; FINITE ELEMENT SOLUTION; MAGNETOSPHERIC FIELD; MAGNETOSPHERIC PHYSICS; NEUMANN BOUNDARY VALUE PROBLEMS; NONCONFORMING FINITE ELEMENT; PIECE-WISE; UNSTRUCTURED GRID;

BOUNDARY VALUE PROBLEMS;

EID: 0005520315     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1999.6206     Document Type: Article

References (24)

1. Alekseev I. I., Shabansky V. P. A model of a magnetic field in the geomagnetosphere. Planet. Space Sci. 20:1972;117.
2. H. Blum, J. Harig, S. Muller, FEAT: Finite element analysis tools, release 1.0, user manual preprint 554, University of Heidelberg, January 1990.
3. Chapman S., Ferraro V. C. A. A new theory of magnetic storms. Nature. 126:1930;129.
4. Eriksson K., Estep D., Hansbo P., Johnson C. Computational Differential Equations. 1996.
5. Hilmer R. V., Voigt G.-H. A magnetospheric magnetic field model with flexible current systems driven by independent physical parameters. J. Geophys. Res. 1995.
6. Klouček P., Luskin M. The computations of the dynamics of the Martensitic deformation. Continuum Mech. Thermodyn. 6:1994.
7. Klouček P., Luskin M. Computational modeling of the Martensitic transformation with surface energy. Math. Comput. Model. 20:1994;101.
8. Klouček P., Li B., Luskin M. Non-conforming finite element approximation of the microstructure. Math. Comp. 65:1996.
9. Koitchev D. K., Kaschiev M. S., Kartelev M. D. Finite element numerical modeling of stationary two-dimensional magnetosphere with defined boundary. J. Comput. Phys. 119:1995;220.
10. M. D. Kartelev, M. S. Kaschiev, D. K. Koitchev, Simplified 3D magnetospheric field, J. Comput. Phys.
11. Moon P., Spencer D. E. Field Theory Handbook. 1988.
12. R. Rannacher, S. Turek, Simple non-conforming quadrilateral Stokes element, Numer. Methods, Partial Differential Equations, 8, 1992.
13. Siscoe G. L. The magnetospheric boundary. Physics of Space Plasmas. 1988;3.
14. Shue J., Chao J. K., Fu H. C., Russell C. T., Song P., Khurana K. K., Singer H. I. A new functional form to study the solar wind control of the magnetopause size and shape. J. Geophys. Res. 102:1997;9497.
15. Stern D. P. Parabolic harmonics in magnetospheric modeling: The main dipole and the ring current. J. Geophys. Res. 90:1985;10,851.
16. Schulz M., McNab M. C. Source-surface model of the magnetosphere. Geophys. Res. Lett. 14:1987;182.
17. Toffoletto F. R., Hill T. W. Mapping of the solar wind electric field to the Earth's polar caps. J. Geophys. Res. 94:1989;329.
18. Toffoletto F. R., Hill T. W. A non-singular model of the open magnetosphere. J. Geophys. Res. 98:1993;1339.
19. Toffoletto F. R., Hilmer R. V., Hill T. W., Voigt G. H. Solution of the Chapman-Ferraro problem with an arbitrary magnetopause. Geophys. Res. Lett. 21:1994;7.
20. Tsyganenko N. A. A solution of the Chapman-Ferraro problem for an ellipsoidal magnetopause. Planet. Space Sci. 37:1989;1037.
21. Tsyganenko N. A. Modeling the Earth's magnetospheric magnetic field confined within a realistic magnetopause. J. Geophys. Res. 100:1995;5599.
22. Voigt G.-H. A three dimensional, analytical magnetospheric model with defined magnetopause. Z. Geophys. 38:1972.
23. G. H. Voigt, Magnetospheric equilibrium configurations and slow adiabatic convection, Solar Wind-Magnetosphere Coupling, Y. KamideJ. A. Slavin, Terra Scientific, Tokyo, 1986, 233.
24. Voigt G.-H. A mathematical magnetospheric field model with independent physical parameters. Planet. Space Sci. 1:1981;29.