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February  2002, 2(1): 95-108. doi: 10.3934/dcdsb.2002.2.95

Finite element analysis and approximations of phase-lock equations of superconductivity

Mei-Qin Zhan 1,

1. 

Department of Mathematics & Statistics, University of North Florida, Jacksonville, FL 32224, United States

Received  March 2001 Revised  September 2001 Published  November 2001

In [22], the author introduced the phase-lock equations and established existences of both strong and weak solutions of the equations. We also investigated the relations between phase-lock equations and Ginzburg-Landau equations of Superconductivity. In this paper, we present finite element analysis and computations of phase-lock equations. We derive the error estimates for both semi-discrete and fully discrete equations, including optimal $L^2$ and $H^1$ error estimates. In the fully discrete case, we use backward Euler method to discretize the time variable.
Keywords: Time Dependent Ginzburg-Landau (TDGL) Equations, error estimates, finite element, phase-pock equations, optimal convergence, backward Euler method., discrete equations.
Mathematics Subject Classification: 35B05, 35B30, 35B6.
Citation: Mei-Qin Zhan. Finite element analysis and approximations of phase-lock equations of superconductivity. Discrete & Continuous Dynamical Systems - B, 2002, 2 (1) : 95-108. doi: 10.3934/dcdsb.2002.2.95
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