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

Bartels, Sören

ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 5, pp. 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.

Classification : 35K59, 35Q99, 53A10
Mots clés : Ginzburg-Landau equations, numerical approximation, error analysis, spectral estimate, finite element method

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