The frozen-field approximation and the Ginzburg-Landau equations of   superconductivity
  The Ginzburg--Landau (GL) equations of superconductivity provide a computational model for the study of magnetic flux vortices in type-II superconductors. In this article we show through numerical examples and rigorous mathematical analysis that the GL model reduces to the frozen-field model when the charge of the Cooper pairs (the superconducting charge carriers) goes to zero while the applied field stays near the upper critical field. 
H. G. Kaper and H. Nordborg