A finite element approximation of a variational inequality formulation of Bean’s model for superconductivity. (English) Zbl 1071.82063
Summary: We introduce a finite element approximation of a variational formulation of Bean’s model for the physical configuration of an infinitely long cylindrical superconductor subject to a transverse magnetic field. We prove an error between the exact solution and the approximate solution for the current density and the magnetic field in appropriate norms of order \(h^{1/2}+\Delta t\). Numerical simulations for a variety of applied magnetic fields are also presented.
MSC:
82D55 | Statistical mechanics of superconductors |
65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
49J40 | Variational inequalities |
74S05 | Finite element methods applied to problems in solid mechanics |
78A25 | Electromagnetic theory (general) |