  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.
