Year: 2005
International Journal of Numerical Analysis and Modeling, Vol. 2 (2005), Iss. 4 : pp. 479–488
Abstract
In this paper we study the numerical solution for an $p$-Laplacian type of evolution system $H_t + \nabla \times [|\nabla \times H|^{p-2} \nabla \times H] = F (x, t)$, $p > 2$ 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2005-IJNAM-942
International Journal of Numerical Analysis and Modeling, Vol. 2 (2005), Iss. 4 : pp. 479–488
Published online: 2005-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: approximation of Bean's critical-state model numerical solutions.