Abstract
The finite difference approximations of the dynamical systems governed by two-dimensional complex Ginzburg–Landau equation was considered. For a fully discrete scheme, the solvability, stability and convergence are proved in discrete Sobolev spaces. Furthermore, the existence of global attractors 𝒜 h, τ of the discrete system and the upper semicontinuity dist(𝒜 h, τ, 𝒜) → 0 are obtained.
ACKNOWLEDGMENTS
Gratitude is extended to Prof. FaYong Zhang for his guidance. Thanks is also offered to Prof. Endre Suli and Prof. Andrew Stuart for many valuable suggestions.