Discrete gauge invariant approximations of a time dependent Ginzburg-Landau model of superconductivity

Abstract

We present here a mathematical analysis of a nonstandard difference method for the numerical solution of the time dependent Ginzburg-Landau models of superconductivity. This type of method has been widely used in numerical simulations of the behavior of superconducting materials. We also illustrate some of their nice properties such as the gauge invariance being retained in discrete approximations and the discrete order parameter having physically consistent pointwise bound.