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Robust a priori error analysis for the approximationof degree-one Ginzburg-Landau vortices

Published online by Cambridge University Press:  15 September 2005

Sören Bartels
Sören Bartels*
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, USA. sba@math.umd.edu
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Abstract

This article discusses the numerical approximation oftime dependent Ginzburg-Landau equations. Optimal error estimates which are robust with respectto a large Ginzburg-Landau parameter are established for asemi-discrete in time and a fully discrete approximationscheme. The proofs rely on an asymptotic expansion of the exact solution and a stability resultfor degree-one Ginzburg-Landau vortices. The error boundsprove that degree-one vortices can be approximated robustlywhile unstable higher degree vortices are critical.

Keywords

Ginzburg-Landau equationsnumerical approximationerror analysisspectral estimatefinite element method.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 5 , September 2005 , pp. 863 - 882
Copyright
© EDP Sciences, SMAI, 2005

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