Robust a priori error analysis for the approximation of degree-one Ginzburg-Landau vortices
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 5, p. 863-882

This article discusses the numerical approximation of time dependent Ginzburg-Landau equations. Optimal error estimates which are robust with respect to a large Ginzburg-Landau parameter are established for a semi-discrete in time and a fully discrete approximation scheme. The proofs rely on an asymptotic expansion of the exact solution and a stability result for degree-one Ginzburg-Landau vortices. The error bounds prove that degree-one vortices can be approximated robustly while unstable higher degree vortices are critical.

DOI : https://doi.org/10.1051/m2an:2005038
Classification:  35K59,  35Q99,  53A10
Keywords: Ginzburg-Landau equations, numerical approximation, error analysis, spectral estimate, finite element method
@article{M2AN_2005__39_5_863_0,
     author = {Bartels, S\"oren},
     title = {Robust a priori error analysis for the approximation of degree-one Ginzburg-Landau vortices},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {5},
     year = {2005},
     pages = {863-882},
     doi = {10.1051/m2an:2005038},
     zbl = {1078.35006},
     mrnumber = {2178565},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2005__39_5_863_0}
}
Bartels, Sören. Robust a priori error analysis for the approximation of degree-one Ginzburg-Landau vortices. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 5, pp. 863-882. doi : 10.1051/m2an:2005038. http://www.numdam.org/item/M2AN_2005__39_5_863_0/

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