TY - JOUR
T1 - Numerical Solutions to Bean's Critical-State Model for Type-II Superconductors
AU - W. Wei & H.-M. Yin
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 479
EP - 488
PY - 2005
DA - 2005/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/942.html
KW - approximation of Bean's critical-state model, numerical solutions.
AB - <p style="text-align: justify;">In this paper we study the numerical solution for an $p$-Laplacian type of evolution system $H_t + \nabla \times [|\nabla \times H|^{p-2} \nabla \times H] = F (x, t)$, $p &gt; 2$ in two space dimensions.
For large $p$ this system is an approximation of Bean&#39;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.</p>