Robust a priori error analysis for the approximation of degree-one Ginzburg-Landau vortices
Department of Mathematics,
University of Maryland, College Park, MD 20742, USA. firstname.lastname@example.org
Revised: 24 May 2005
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.
Mathematics Subject Classification: 35K59 / 35Q99 / 53A10
Key words: Ginzburg-Landau equations / numerical approximation / error analysis / spectral estimate / finite element method.
© EDP Sciences, SMAI, 2005