The Ginzburg-Landau Equation Solved by the Finite Element Method

    Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearch


    Around 1950 V.L. Ginzburg and L.D. Landau proposed a phenomenological theory for phase transitions1. The theory is based on a phenomenological Schrödinger equation with a φ-4 potential and a kinetic term involving the momentum operator. One of the more successful applications of the theory is to superconductivity and in particular to superconductors placed in a magnetic field. Superconductors expel magnetic fields from the inside bulk by setting up screening currents in the surface (type I superconductors). However, some supercon-ductors allow for magnetic field penetration through quantized current vortices when the magnetic field exceeds a threshold value. These superconductors are called type II supercon-ductors. In this article we solve numerically the time dependent Ginzburg-Landau equation coupled to a magnetic field for type II superconductors of complex geometry, where the finite element method is particularly suited.
    Original languageEnglish
    Title of host publicationProceedings of the Comsol Conference
    EditorsLars Gregersen
    Number of pages150
    Place of PublicationCopenhagen, Denmark
    PublisherCOMSOL Inc.
    Publication date2006
    ISBN (Print)87-989426-1-1
    Publication statusPublished - 2006
    EventNordic Comsol Conference - Kgs. Lyngby, Denmark
    Duration: 1 Nov 20062 Nov 2006


    ConferenceNordic Comsol Conference
    CityKgs. Lyngby


    • nonlinear dynamics
    • phase transition
    • Ginzburg-Landau model
    • Superconductivity


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