Numerical solution of the three-dimensional Ginzburg-Landau models using artificial boundary

For three-dimensional simulations of the vortex phenomena in superconductors based on the Ginzburg-Landau (GL) theory, the physical variables must be solved in the whole space in general. Exact boundary conditions on an artificial boundary are discussed to reformulate the problem in a finite domain. Approximations of these boundary conditions with high accuracy are given, and their convergence properties are examined. Error estimates are derived for the finite element approximations with the approximate boundary conditions