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An A-ϕ Scheme for Type-II Superconductors

Published online by Cambridge University Press:  31 January 2018

Tao Chen*
Affiliation:
School of Sciences, Communication University of China, Beijing 100024, China
Tong Kang*
Affiliation:
School of Sciences, Communication University of China, Beijing 100024, China
Jun Li*
Affiliation:
School of Sciences, Communication University of China, Beijing 100024, China
*
*Corresponding author. Email addresses:chentao@cuc.edu.cn (T. Chen), kangtong@cuc.edu.cn (T. Kang), lijun@cuc.edu.cn (J. Li)
*Corresponding author. Email addresses:chentao@cuc.edu.cn (T. Chen), kangtong@cuc.edu.cn (T. Kang), lijun@cuc.edu.cn (J. Li)
*Corresponding author. Email addresses:chentao@cuc.edu.cn (T. Chen), kangtong@cuc.edu.cn (T. Kang), lijun@cuc.edu.cn (J. Li)
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Abstract

A fully discrete A-ϕ finite element scheme for a nonlinear model of type-II superconductors is proposed and analyzed. The nonlinearity is due to a field dependent conductivity with the regularized power-law form. The challenge of this model is the error estimate for the nonlinear term under the time derivative. Applying the backward Euler method in time discretisation, the well-posedness of the approximation problem is given based on the theory of monotone operators. The fully discrete system is derived by standard finite element method. The error estimate is suboptimal in time and space.

MSC classification

Type
Research Article
Copyright
Copyright © Global-Science Press 2017 

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References

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