Numerical Solution of the Three-Dimensional Ginzburg-Landau Models Using Artificial Boundary

Qiang Du*, Xiaonan Wu

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

10 Citations (Scopus)
25 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)1482-1506
Number of pages25
JournalSIAM Journal on Numerical Analysis
Issue number5
Publication statusPublished - Sept 1999

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Artificial boundary
  • Convergence
  • Finite element method
  • Ginzburg-Landau equations
  • H and l error estimates
  • Superconductivity
  • Unbounded domain


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