no. 3
An upwinding mixed finite element method for a mean field model of superconducting vortices
ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 3, pp. 687-706. 
@article{M2AN_2000__34_3_687_0,
     author = {Chen, Zhiming and Du, Qiang},
     title = {An upwinding mixed finite element method for a mean field model of superconducting vortices},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {687--706},
     publisher = {Dunod},
     address = {Paris},
     volume = {34},
     number = {3},
     year = {2000},
     mrnumber = {1763531},
     zbl = {1078.82548},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2000__34_3_687_0/}
}
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Chen, Zhiming; Du, Qiang. An upwinding mixed finite element method for a mean field model of superconducting vortices. ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 3, pp. 687-706. http://www.numdam.org/item/M2AN_2000__34_3_687_0/

[1] S. C. Brenner and L. R. Scott, The mathematical theory of finite element methods. Springer-Verlag, New York (1994). | MR | Zbl

[2] F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer, New York (1991). | MR | Zbl

[3] S. J. Chapman, A mean-field model of superconductmg vortices in three dimensions. SIAM J. Appl. Math. 55 (1995)1259-1274. | MR | Zbl

[4] S. J. Chapman and G. Richardson, Motion of vortices in type-II superconductors. SIAM J. Appl. Math. 55 (1995) 1275-1296. | MR | Zbl

[5] S. J. Chapman, J. Rubenstem, and M. Schatzman, A mean-field model of superconducting vortices. Euro J. Appl. Math. 7 (1996) 97-111. | MR | Zbl

[6] Z. Chen and S. Dai, Adaptive Galerkin methods with error control for a dynamical Ginzburg-Landau model in superconductwity. (Preprint, 1998). | MR | Zbl

[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. | MR | Zbl

[8] Q. Du, Convergence analysis of a hybrid numerical method for a mean field model of superconducting vortices. SIAM Numer. Analysis, (1998).

[9] Q. Du, M. Gunzburger, and J. Peterson, Analysis and approximation of the Ginzburg-Landau model of superconductivity. SIAM Review 34 (1992) 54-81. | MR | Zbl

[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] Q. Du,M. Gunzburger and H. Lee, Analysis and computation of a mean field model for superconductivity. Numer. Math. 81 539-560 (1999). | MR | Zbl

[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. | MR | Zbl

[13] W. E, Dynamics of vortices in Ginzburg-Landau theories with applications to superconductivity. Phys. D. 77 (1994) 383-404. | MR | Zbl

[14] C. Elliott and V. Styles, Numerical analysis of a mean field model of superconductivity, preprint.

[15] V. Girault and -A. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer, Berlin (1986). | MR | Zbl

[16] Grisvard, Elliptic Problems on Non-smooth Domains. Pitman, Boston (1985). | Zbl

[17] C. Huang and T. Svobodny, Evolution of Mixed-state Régions in type-II superconductors. SIAM J. Math. Anal. 29 (1998) 1002-1021. | MR | Zbl

[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). | Zbl

[19] L. Prigozhin, On the Bean critical-state model of superconductivity. Euro J. Appl. Math. 7 (1996) 237-247. | MR | Zbl

[20] L. Prigozhin, The Bean model in superconductivity variational formulation and numerical solution. J. Com. Phys. 129 (1996) 190-200. | MR | Zbl

[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). | Zbl

[22]R. Schatale and V. Styles, Analysis of a mean field model of superconducting vortices, (preprint). | Zbl

[23] R. Temam, Navier-Stokes equations, Theory and Numerical Analysis North-Holland, Amsterdam (1984). | MR | Zbl