Self-consistent Ginzburg-Landau theory for transport currents in   superconductors
  We elaborate on boundary conditions for Ginzburg-Landau (GL) theory in the case of external currents. We implement a self-consistent theory within the finite element method (FEM) and present numerical results for a two-dimensional rectangular geometry. We emphasize that our approach can in principle also be used for general geometries in three-dimensional superconductors. 
M. Ogren, M. P. Soerensen, N. F. Pedersen
cond-mat.supr-con physics.comp-ph