Mixed finite element methods for a dynamical Ginzburg-Landau model in superconductivity

Summary.

In this paper we consider the numerical solutions of the nonlinear time-dependent Ginzburg-Landau model which describes the phase transitions taking place in superconducting films. We propose a semi-implicit finite element scheme which is based on a linear finite element approximation of the order parameter $\psi$ and a mixed finite element discretization for the equation involving the magnetic potential A. The error estimates of the scheme are derived.