Free Access
Issue
ESAIM: M2AN
Volume 42, Number 3, May-June 2008
Page(s) 333 - 374
DOI https://doi.org/10.1051/m2an:2008010
Published online 03 April 2008
  1. H. Attouch, Variational Convergence for Functions and Operators. Pitman Advanced Publishing Program, Boston-London-Melbourne (1984). [Google Scholar]
  2. H. Attouch and A. Damlamian, Application des méthodes de convexité et monotonie à l'étude de certaines équations quasi-linéaires. Proc. Roy. Soc. Edinburgh 79A (1977) 107–129. [Google Scholar]
  3. A. Badía and C. López, Critical state theory for nonparallel flux line lattices in type-II superconductors. Phys. Rev. Lett. 87 (2001) 127004. [CrossRef] [PubMed] [Google Scholar]
  4. A. Badía and C. López, Vector magnetic hysteresis of hard superconductors. Phys. Rev. B 65 (2002) 104514. [CrossRef] [Google Scholar]
  5. A. Badía and C. López, The critical state in type-II superconductors with cross-flow effects. J. Low. Temp. Phys. 130 (2003) 129–153. [Google Scholar]
  6. J.W. Barrett and L. Prigozhin, Dual formulations in critical state problems. Interfaces Free Boundaries 8 (2006) 349–370. [CrossRef] [Google Scholar]
  7. C.P. Bean, Magnetization of high-field superconductors. Rev. Mod. Phys. 36 (1964) 31–39. [CrossRef] [Google Scholar]
  8. A. Bermúdez, R. Rodríguez and P. Salgado, A finite element method with Lagrange multipliers for low-frequency harmonic Maxwell equations. SIAM J. Num. Anal. 40 (2002) 1823–1849. [CrossRef] [MathSciNet] [Google Scholar]
  9. A. Bossavit, Numerical modelling of superconductors in three dimensions: a model and a finite element method. IEEE Trans. Magn. 30 (1994) 3363–3366. [CrossRef] [Google Scholar]
  10. H. Brezis, Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations, in Contributions to Nonlinear Functional Analysis, E. Zarantonello Ed., Academic Press, Madison, WI (1971) 101–156. [Google Scholar]
  11. S.J. Chapman, A hierarchy of models for type-II superconductors. SIAM Rev. 42 (2000) 555–598. [CrossRef] [MathSciNet] [Google Scholar]
  12. J.R. Clem and A. Perez-Gonzalez, Flux-line-cutting and flux-pinning losses in type-II superconductors in rotating magnetic fields. Phys. Rev. B 30 (1984) 5041–5047. [CrossRef] [Google Scholar]
  13. I. Ekeland and R. Temam, Convex Analysis and Variational Problems. North-Holland Publishing Co., Amsterdam (1976). [Google Scholar]
  14. C.M. Elliott and Y. Kashima, A finite-element analysis of critical-state models for type-II superconductivity in 3D. IMA J. Num. Anal. 27 (2007) 293–331. [CrossRef] [Google Scholar]
  15. C.M. Elliott, D. Kay and V. Styles, A finite element approximation of a variational formulation of Bean's model for superconductivity. SIAM J. Num. Anal. 42 (2004) 1324–1341. [CrossRef] [Google Scholar]
  16. C.M. Elliott, D. Kay and V. Styles, Finite element analysis of a current density – electric field formulation of Bean's model for superconductivity. IMA J. Num. Anal. 25 (2005) 182–204. [CrossRef] [Google Scholar]
  17. V. Girault and P.A. Raviart, Finite element methods for Navier-Stokes equations, Theory and algorithms. Springer, Berlin (1986). [Google Scholar]
  18. S. Guillaume and A. Syam, On a time-dependent subdifferential evolution inclusion with a nonconvex upper-semicontinuous perturbation. E. J. Qualitative Theory Diff. Equ. 11 (2005) 1–22. [Google Scholar]
  19. Y. Kashima, Numerical analysis of macroscopic critical state models for type-II superconductivity in 3D. Ph.D. thesis, University of Sussex, Brighton, UK (2006). [Google Scholar]
  20. N. Kenmochi, Solvability of Nonlinear Evolution Equations with Time-Dependent Constraints and Applications, The Bulletin of The Faculty of Education 30. Chiba University, Chiba, Japan (1981). [Google Scholar]
  21. P. Monk, Finite element methods for Maxwell's equations. Oxford University Press, Oxford (2003). [Google Scholar]
  22. J.C. Nédélec, Mixed finite elements in Formula . Numer. Math. 35 (1980) 315–341. [CrossRef] [MathSciNet] [Google Scholar]
  23. A. Perez-Gonzalez and J.R. Clem, Response of type-II superconductors subjected to parallel rotating magnetic fields. Phys. Rev. B 31 (1985) 7048–7058. [CrossRef] [Google Scholar]
  24. A. Perez-Gonzalez and J.R. Clem, Magnetic response of type-II superconductors subjected to large-amplitude parallel magnetic fields varying in both magnitude and direction. J. Appl. Phys. 58 (1985) 4326–4335. [CrossRef] [Google Scholar]
  25. A. Perez-Gonzalez and J.R. Clem, ac losses in type-II superconductors in parallel magnetic fields. Phys. Rev. B 32 (1985) 2909–2914. [CrossRef] [Google Scholar]
  26. L. Prigozhin, On the Bean critical-state model in superconductivity. Eur. J. Appl. Math. 7 (1996) 237–247. [Google Scholar]
  27. L. Prigozhin, The Bean model in superconductivity: variational formulation and numerical solution. J. Comput. Phys. 129 (1996) 190–200. [CrossRef] [MathSciNet] [Google Scholar]
  28. L. Prigozhin, Solution of thin film magnetization problems in type-II superconductivity. J. Comput. Phys. 144 (1998) 180–193. [CrossRef] [MathSciNet] [Google Scholar]
  29. J. Rhyner, Magnetic properties and AC-losses of superconductors with power law current-voltage characteristics. Physica C 212 (1993) 292–300. [CrossRef] [Google Scholar]
  30. R.T. Rockafellar, Integrals which are convex functionals. Pacific J. Math. 24 (1968) 525–539. [Google Scholar]
  31. R.T. Rockafellar and R.J.-B. Wets, Variational analysis. Springer, Berlin-Heidelberg-New York (1998). [Google Scholar]
  32. R. Rossi and G. Savaré, Tightness, integral equicontinuity and compactness for evolution problems in Banach spaces. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 5 (2003) 395–431. [Google Scholar]
  33. W. Rudin, Functional analysis. McGraw-Hill, New York-Tokyo (1991). [Google Scholar]
  34. A. Schmidt and K.G. Siebert, Design of adaptive finite element software, the finite element toolbox ALBERTA, Lect. Notes Comput. Sci. Engrg. 42. Springer, Berlin-Heidelberg (2005). [Google Scholar]
  35. H. Si, TetGen: A Quality Tetrahedral Mesh Generator and Three-Dimensional Delaunay Triangular. Version 1.4.1 (http://tetgen.berlios.de), Berlin (2006). [Google Scholar]
  36. J. Simon, Compact sets in the space Lp(0,T;B). Ann. Math. Pure. Appl. 146 (1987) 65–96. [Google Scholar]
  37. V. Thomée, Galerkin finite element methods for parabolic problems. Springer, Berlin (1997). [Google Scholar]
  38. S. Yotsutani, Evolution equations associated with the subdifferentials. J. Math. Soc. Japan 31 (1978) 623–646. [CrossRef] [Google Scholar]

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