An upwinding mixed finite element method for a mean field model of superconducting vortices

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1. [1] S. C. Brenner and L. R. Scott, The mathematical theory of finite element methods. Springer-Verlag, New York (1994). Zbl0804.65101MR1278258
2. [2] F. Brezzi and M. Fortin,Mixed and Hybrid Finite Element Methods. Springer, New York (1991). Zbl0788.73002MR1115205
3. [3] S. J. Chapman, A mean-field model of superconductmg vortices in three dimensions. SIAM J. Appl. Math. 55 (1995)1259-1274. Zbl0836.76014MR1349309
4. [4] S. J. Chapman and G. Richardson, Motion of vortices in type-II superconductors. SIAM J. Appl. Math. 55 (1995) 1275-1296. Zbl0836.76015MR1349310
5. [5] S. J. Chapman, J. Rubenstem, and M. Schatzman, A mean-field model of superconducting vortices. Euro J. Appl. Math. 7 (1996) 97-111. Zbl0849.35135MR1388106
6. [6] Z. Chen and S. Dai, Adaptive Galerkin methods with error control for a dynamical Ginzburg-Landau model in superconductwity. (Preprint, 1998). Zbl0987.65096MR1856238
7. [7] B. Cockburn, S. Hou and C.-W. Shu, The Runge-Kutta local project ion discontinuos galerkin finite element method for conservation laws IV: The multidimensional case. Math. Com. 54 (1990) 545-581. Zbl0695.65066MR1010597
8. [8] Q. Du, Convergence analysis of a hybrid numerical method for a mean field model of superconducting vortices. SIAM Numer. Analysis, (1998). 
9. [9] Q. Du, M. Gunzburger, and J. Peterson, Analysis and approximation of the Ginzburg-Landau model of superconductivity. SIAM Review 34 (1992) 54-81. Zbl0787.65091MR1156289
10. [10] Q. Du, M. Gunzburger, and J. Peterson, Computational simulations of type-II superconductivity including pinnnig mechanisms. Phys. Rev. B 51 (1995) 16194-16203. 
11. [11] Q. Du, M. Gunzburger and H. Lee, Analysis and computation of a mean field model for superconductivity. Numer. Math. 81 539-560 (1999). Zbl0922.65090MR1675208
12. [12] Q. Du and Gray, High-kappa limit of the time dependent Ginzburg-Landau model for superconductivity. SIAM J. Appl. Math. 56 (1996) 1060-1093. Zbl0865.35119MR1398408
13. [13] W. E, Dynamics of vortices in Ginzburg-Landau theories with applications to superconductivity. Phys. D. 77 (1994) 383-404. Zbl0814.34039MR1297726
14. [14] C. Elliott and V. Styles, Numerical analysis of a mean field model of superconductivity, preprint. Zbl0984.82042
15. [15] V. Girault and -A. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer, Berlin (1986). Zbl0585.65077MR851383
16. [16] Grisvard, Elliptic Problems on Non-smooth Domains. Pitman, Boston (1985). Zbl0695.35060
17. [17] C. Huang and T. Svobodny, Evolution of Mixed-state Régions in type-II superconductors. SIAM J. Math. Anal. 29 (1998) 1002-1021. Zbl0924.76116MR1617698
18. [18] Lesaint and P. A. Raviart, On a Finite Element Method for Solving the Neutron Transport equation, in Mathematical Aspects of the Finite Element Method in Partial Differential Equations, C. de Boor Ed., Academic Press, New York (1974). Zbl0341.65076
19. [19] L. Prigozhin, On the Bean critical-state model of superconductivity. Euro J. Appl. Math. 7 (1996) 237-247. Zbl0873.49007MR1401169
20. [20] L. Prigozhin, The Bean model in superconductivity variational formulation and numerical solution. J. Com. Phys. 129 (1996) 190-200. Zbl0866.65081MR1419742
21. [21] Raviart and J. Thomas, A mixed element method for 2nd order elliptic problems, in Mathematical Aspects of the Finite Element Method) Lecture Notes on Mathematics, Springer, Berlin 606 (1977). Zbl0362.65089
22. [22] R. Schatale and V. Styles, Analysis of a mean field model of superconducting vortices, (preprint). Zbl0941.35133
23. [23] R. Temam, Navier-Stokes equations, Theory and Numerical Analysis North-Holland, Amsterdam (1984). Zbl0568.35002MR769654