Finite Element Methods for the Time-Dependent Ginzburg-Landau Model of Superconductivity

The initial-boundary value problem for the time-dependent Ginzburg-Landau equa, tions that model the macroscopic behavior of superconductors is considered. The convergence of finite-dimensional, semidiscrete Galerkin approximations is studied as is a fully-discrete scheme. The results of some computational experiments are presented. Keywords-Superconductivity, Timedependent Ginzburg-Landau equations, Finite element methods. 1. THE TIME-DEPENDENT GINZBURG-LANDAU EQUATIONS The steady state Ginzburg-Landau model for superconductivity (see, e.g., [l] or [2]) was extended to the time-dependent case by Gor’kov and Eliashberg in [3]. The latter model is defined by the differential equations vg+ivnQi+ (AV+A)2~-~+1~[2~=0, inRx[O,T],