Numerical Solutions to Bean’s Critical-state Model for Type-ii Superconductors

In this paper we study the numerical solution for an p−Laplacian type of evolution system Ht + ∇ × [|∇ × H|p−2∇ × H] = F(x, t), p > 2 in two space dimensions. For large p this system is an approximation of Bean’s critical-state model for type-II superconductors. By introducing suitable transformation, the system is equivalent to a nonlinear parabolic equation. For the nonlinear parabolic problem we obtain the numerical solution by combining approximation schemes for the linear equation and the nonlinear semigroup. The convergence and stability of the scheme are proved. Finally, a numerical experiment is presented.