Virginia TechDu, Q.Gunzburger, Max D.Peterson, Janet S.2014-05-072014-05-071992-10Du, Q.; Gunzburger, M. D.; Peterson, J. S., "Solving the Ginzburg-Landau equations by finite-element methods," Phys. Rev. B 46, 9027 DOI: http://dx.doi.org/10.1103/PhysRevB.46.90270163-1829http://hdl.handle.net/10919/47888We 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.en-USIn Copyrightii superconductorsphysics, condensed matterArticle - Refereedhttp://journals.aps.org/prb/abstract/10.1103/PhysRevB.46.9027https://doi.org/10.1103/PhysRevB.46.9027