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

Sören Bartels

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 39, Issue: 5, page 863-882
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Bartels, Sören. "Robust a priori error analysis for the approximation of degree-one Ginzburg-Landau vortices." ESAIM: Mathematical Modelling and Numerical Analysis 39.5 (2010): 863-882. <http://eudml.org/doc/194291>.

@article{Bartels2010,
abstract = { 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. },
author = {Bartels, Sören},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Ginzburg-Landau equations; numerical approximation; error analysis; spectral estimate; finite element method.; error analysis},
language = {eng},
month = {3},
number = {5},
pages = {863-882},
publisher = {EDP Sciences},
title = {Robust a priori error analysis for the approximation of degree-one Ginzburg-Landau vortices},
url = {http://eudml.org/doc/194291},
volume = {39},
year = {2010},
}

TY - JOUR
AU - Bartels, Sören
TI - Robust a priori error analysis for the approximation of degree-one Ginzburg-Landau vortices
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 39
IS - 5
SP - 863
EP - 882
AB - 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.
LA - eng
KW - Ginzburg-Landau equations; numerical approximation; error analysis; spectral estimate; finite element method.; error analysis
UR - http://eudml.org/doc/194291
ER -

References

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