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The Bean model in superconductivity: Variational formulation and numerical solution. (English) Zbl 0866.65081

The author derives and discusses a quasivariational problem the solution of which is the difference between an external magnetic field and the full magnetic field acting on a superconducting medium. The unilateral condition restricting the solution is an upper bound on the current density. An equivalent formulation for the current density is obtained which corresponds to the bounded domain occupied by the superconductor.
Two cases are considered in more detail (including numerical results based on finite difference discretization in time and finite elements in space, solving the resulting constrained optimization problem by underrelaxation): the case of two-dimensional and that of axially symmetric current distribution.

MSC:

65Z05 Applications to the sciences
35Q60 PDEs in connection with optics and electromagnetic theory
65N06 Finite difference methods for boundary value problems involving PDEs
78A25 Electromagnetic theory (general)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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