Fourier spectral approximation to long-time behavior of three dimensional Ginzburg-Landau type equation (Q2454720)

A Ginzburg-Landau type equation, a kind of a nonlinear evolution equation, with a periodic initial value condition in three-dimensional domains is considered. A fully discrete Galerkin-Fourier spectral approximation scheme is presented. The authors prove the existence of global attractors of the discrete system and their convergence. Hereby, a priori estimates and error estimates of the discrete solution are used. Furthermore, the numerical stability of the discrete scheme is shown and the long-time convergence of the discrete scheme is proved.