Free Access
Volume 42, Number 3, May-June 2008
Page(s) 333 - 374
Published online 03 April 2008
  1. H. Attouch, Variational Convergence for Functions and Operators. Pitman Advanced Publishing Program, Boston-London-Melbourne (1984).
  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.
  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]
  4. A. Badía and C. López, Vector magnetic hysteresis of hard superconductors. Phys. Rev. B 65 (2002) 104514. [CrossRef]
  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.
  6. J.W. Barrett and L. Prigozhin, Dual formulations in critical state problems. Interfaces Free Boundaries 8 (2006) 349–370. [CrossRef]
  7. C.P. Bean, Magnetization of high-field superconductors. Rev. Mod. Phys. 36 (1964) 31–39. [CrossRef]
  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]
  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]
  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.
  11. S.J. Chapman, A hierarchy of models for type-II superconductors. SIAM Rev. 42 (2000) 555–598. [CrossRef] [MathSciNet]
  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]
  13. I. Ekeland and R. Temam, Convex Analysis and Variational Problems. North-Holland Publishing Co., Amsterdam (1976).
  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]
  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]
  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]
  17. V. Girault and P.A. Raviart, Finite element methods for Navier-Stokes equations, Theory and algorithms. Springer, Berlin (1986).
  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.
  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).
  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).
  21. P. Monk, Finite element methods for Maxwell's equations. Oxford University Press, Oxford (2003).
  22. J.C. Nédélec, Mixed finite elements in Formula . Numer. Math. 35 (1980) 315–341. [CrossRef] [MathSciNet]
  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]
  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]
  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]
  26. L. Prigozhin, On the Bean critical-state model in superconductivity. Eur. J. Appl. Math. 7 (1996) 237–247.
  27. L. Prigozhin, The Bean model in superconductivity: variational formulation and numerical solution. J. Comput. Phys. 129 (1996) 190–200. [CrossRef] [MathSciNet]
  28. L. Prigozhin, Solution of thin film magnetization problems in type-II superconductivity. J. Comput. Phys. 144 (1998) 180–193. [CrossRef] [MathSciNet]
  29. J. Rhyner, Magnetic properties and AC-losses of superconductors with power law current-voltage characteristics. Physica C 212 (1993) 292–300. [CrossRef]
  30. R.T. Rockafellar, Integrals which are convex functionals. Pacific J. Math. 24 (1968) 525–539.
  31. R.T. Rockafellar and R.J.-B. Wets, Variational analysis. Springer, Berlin-Heidelberg-New York (1998).
  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.
  33. W. Rudin, Functional analysis. McGraw-Hill, New York-Tokyo (1991).
  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).
  35. H. Si, TetGen: A Quality Tetrahedral Mesh Generator and Three-Dimensional Delaunay Triangular. Version 1.4.1 (, Berlin (2006).
  36. J. Simon, Compact sets in the space Lp(0,T;B). Ann. Math. Pure. Appl. 146 (1987) 65–96.
  37. V. Thomée, Galerkin finite element methods for parabolic problems. Springer, Berlin (1997).
  38. S. Yotsutani, Evolution equations associated with the subdifferentials. J. Math. Soc. Japan 31 (1978) 623–646. [CrossRef]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you