Solving the Ginzburg-Landau equations by finite-element methods

Phys. Rev. B 46, 9027 – Published 1 October 1992
Q. Du, M. D. Gunzburger, and J. S. Peterson

Abstract

We consider finite-element methods for the approximation of solutions of the Ginzburg-Landau equations of superconductivity. The methods are based on a discretization of the Euler-Lagrange equations resulting from the minimization of the free-energy functional. The discretization is effected by requiring the approximate solution to be a piecewise polynomial with respect to a grid. The magnetization versus magnetic field curves obtained through the finite-element methods agree well with analogous calculations obtained by other schemes. We demonstrate, both by analyzing the algorithms and through computational experiments, that finite-element methods can be very effective and efficient means for the computational simulation of superconductivity phenomena and therefore could be applied to determine macroscopic properties of inhomogeneous, anisotropic superconductors.

DOI: http://dx.doi.org/10.1103/PhysRevB.46.9027

  • Received 10 February 1992
  • Published in the issue dated 1 October 1992

© 1992 The American Physical Society

Authors & Affiliations

Q. Du

  • Department of Mathematics, Michigan State University, East Lansing, Michigan 48224

M. D. Gunzburger and J. S. Peterson

  • Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061

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