Numerical studies of a non-stationary Ginzburg-Landau model for superconductivity. (English) Zbl 0846.65051

Chen, Zhiming; Hoffmann, K.-H.

Adv. Math. Sci. Appl. 5, No. 2, 363-389 (1995).

This paper is devoted to the numerical solution of a system of nonlinear parabolic equations coming from the Ginzburg-Landau theory in the modelling of superconductivity phase transitions. A discrete finite element scheme is proposed. Some stability estimates are shown and an error estimate for the scheme is demonstrated. A numerical example is given.

Reviewer: Laura-Iulia Aniţa (Iaşi)

MSC:

65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q72	Other PDE from mechanics (MSC2000)
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15	Error bounds for initial value and initial-boundary value problems involving PDEs
82D55	Statistical mechanics of superconductors

Keywords:

Ginzburg-Landau equation; nonlinear system; superconductivity phase transitions; finite element; stability; error estimate; numerical example