Finite element analysis on the Lawrence-Doniach model for layered superconductors

Numerical Functional Analysis and Optimization

Volumn 18, Issue 5-6, 1997, Pages 567-589

  Hoffmann, K H ^a   Zou, Jun ^b  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

ERROR ANALYSIS; ESTIMATION; MATHEMATICAL MODELS; SUPERCONDUCTING MATERIALS;

LAWRENCE DONIACH MODEL; LAYERED SUPERCONDUCTORS;

FINITE ELEMENT METHOD;

EID: 0031187562     PISSN: 01630563     EISSN: None     Source Type: Journal    
DOI: 10.1080/01630569708816779     Document Type: Article

References (32)

1. J. Bardeen, L. Cooper and J. Schrieffer. Theory of superconductivity. Phys. Review, 108:1175-1204, 1957.
2. L.N. Bulaevskii. Magnetic properties of layered superconductors with weak interaction between the layers. Zh. Èksper. Teoret. Fiz., 64:2241-2247, 1973.
3. J. Chapman, Q. Du and M. Gunzburger. On the Lawrence-Doniach and anisotropic Ginzburg-Landau models for layered superconductors. SIAM J. Appl. Math., 55:156-174, 1995.
4. S. Chapman, S. Howison and J. Ockendon. Macroscopic models for superconductivity. SIAM Review, 34:529-560, 1992.
5. Z. Chen, C. Elliott and Q. Tang. Justification of a two-dimensional evolutionary Ginzburg-Landau superconductivity model. Technical report, 1996.
6. Z. Chen and K.-H. Hoffmann. Numerical studies of a non-stationary Ginzburg-Landau model for superconductivity. Adv. Math. Sci. Appl., 5:363-389, 1995.
7. Z. Chen, K.-H. Hoffmann and L. Jiang. On the Lawrence-Doniach model for layered superconductors. Euro. J. Appl. Math., 1996. to appear.
8. Z. Chen, K.-H. Hoffmann and J. Liang. On a non-stationary Ginzburg-Landau superconductivity model. Math. Meth. Appl. Sci., 16:855-875, 1993.
9. P. Ciarlet. The Finite Element Method for Elliptic Problems. North-Holland, 1978.
10. P. Ciarlet, Jr. and J. Zou. Finite element convergence for the Darwin model to Maxwell's equations. To appear in RAIRO Math. Modelling Numer. Anal.
11. 2-projection onto finite element function spaces. Math. Comp., 48:521-532, 1987.
12. Q. Du. Finite element methods for the time dependent Ginzburg-Landau model of superconductivity. Comp. Math. Appl., 27:119-133, 1994.
13. Q. Du. Global existence and uniqueness of solutions of the time-dependent Ginzburg-Landau model of superconductivity. Applicable Anal., 53:1-17, 1994.
14. Q. Du and P. Gray. High kappa limit of the time dependent Ginzburg-Landau model for superconductivity. SIAM J. Appl. Math. to appear.
15. Q. Du, M. Gunzburger and J. Peterson. Analysis and approximation of Ginzburg-Landau models for superconductivity. SIAM Review, 34:54-81, 1992.
16. Q. Du, M. Gunzburger and J. Peterson. Finite element approximation of a periodic Ginzburg-Landau model for type-II superconductors. Numer. Math., 64:85-114, 1993.
17. Q. Du, M. Gunzburger and J. Peterson. Computational simulations of type-II superconductivity including pinning mechanisms. Phy. Review B, 51:16194-16203, 1995.
18. Q. Du and F.-H. Lin. Ginzburg-Landau vortices: dynamics, pinning and hysteresis. SIAM J. Math. Anal., 1996. to appear.
19. C. Elliott and Q. Tang. Existence theorems for an evolutionary superconductivity model, to appear.
20. V. Ginzburg and L. Landau. On the theory of superconductivity. Zh. Èksper. Teoret. Fiz., 20:1064-1082, 1950. [English translation in Man of Physics: L.D. Landau, D. ter Haar, ed., Pergamon, Oxford (1965), pp. 138-167.
21. V. Ginzburg and L. Landau. On the theory of superconductivity. Zh. Èksper. Teoret. Fiz., 20:1064-1082, 1950. [English translation in Man of Physics: L.D. Landau, D. ter Haar, ed., Pergamon, Oxford (1965), pp. 138-167.
22. V. Girault and P.A. Raviart. Finite Element Methods for Navier-Stokes Equations. Springer-Verlag, Berlin, 1986.
23. L. Gor'kov. Microscopic derivation of the Ginzburg-Landau equations in the theory of superconductivity. Zh. Èkspoer. Teoret. Fiz., 36:1918-1923, 1959. English translation in Soviet Phys. -JEPT 9 (1959), pp. 1364-1367.
24. L. Gor'kov. Microscopic derivation of the Ginzburg-Landau equations in the theory of superconductivity. Zh. Èkspoer. Teoret. Fiz., 36:1918-1923, 1959. English translation in Soviet Phys. -JEPT 9 (1959), pp. 1364-1367.
25. L.P. Gor'kov and G.M. Èliashberg. Generalization of the Ginzburg-Landau equations for non-stationary problems in the case of alloys with paramagnetic impurities. Soviet Phys. - JEPT, 27:328-334, 1968.
26. K.-H. Hoffmann and J. Zou. Finite element approximations of Landau-Ginzburg model for structural phase transitions in shape memory alloys. RAIRO Math. Modelling Numer. Anal., 29:629-655, 1995.
27. R.A. Klemm, A. Luther and M.R. Beasley. Theory of the upper critical field in layered superconductors. Phys. Review B, 12:877-891, 1975.
28. O.A. Ladyzhenskaya, V.A. Solonnikov and N.N. Uralceva. Linear and Quasilinear Equations of Parabolic Type. American Mathematical Society, Providence, 1968.
29. W. Lawrence and S. Doniach. Theory of layer structure superconductors. In Proceedings of the twelfth international conference on low temperature physics, E. Kanda, editor, pages 361-362, Kyoto, 1971. Academic Press of Japan.
30. M. Mu. A linearized Crank-Nicolson-Galerkin method for the Ginzburg-Landau model. SIAM J. Sci. Comput., to appear.
31. T. Tsuzuki. On the long-range order in superconducting intercalated layer compounds. J. Low Temp. Phys., 9:525-538, 1972.
32. J. Xu. Theory of multilevel methods. PhD thesis, Cornell University, May 1989.