Discrete gauge invariant approximations of

a time dependent Ginzburg-Landau model of superconductivity

Author:
Qiang Du

Journal:
Math. Comp. **67** (1998), 965-986

MSC (1991):
Primary 65M12, 65M15; Secondary 82D55

DOI:
https://doi.org/10.1090/S0025-5718-98-00954-5

MathSciNet review:
1464143

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

**Qiang Du**

Affiliation:
Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong and Department of Mathematics, Iowa State University, Ames, Iowa 50011

Email:
madu@uxmail.ust.hk

DOI:
https://doi.org/10.1090/S0025-5718-98-00954-5

Keywords:
Ginzburg-Landau model of superconductivity,
time dependent equations,
nonstandard difference approximations,
gauge invariance,
convergence,
error estimates

Received by editor(s):
June 13, 1996

Received by editor(s) in revised form:
February 19, 1997

Additional Notes:
Research is supported in part by the U. S. National Science Foundation grant MS-9500718 and in part by the HKUST grant DAG 95/96.SC18.

Article copyright:
© Copyright 1998
American Mathematical Society