Solving the Ginzburg-Landau equations by finite-element methods

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

  • Received 10 February 1992


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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Vol. 46, Iss. 14 — 1 October 1992

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