This article is concerned with the Ginzburg-Landau (GL) equations of superconductivity. The equations provide a mathematical model for the study of magnetic flux vortices in superconductors. The focus is on the asymptotic case when the charge of the superconducting charge carriers (Cooper pairs) is vanishingly small and the applied magnetic field approaches the upper critical field. It is shown that the GL model reduces in the limit to the frozen-field model, where the superconducting phenomena are affected by the electromagnetic phenomena, but not vice versa. The convergence is second order in the small parameter. The analytical results are confirmed in some numerical examples.

}, author = {H. G. Kaper and H. Nordborg} }