Discrete gevrey regularity attractors and uppers–semicontinuity for a finite difference approximation to the ginzburg–landau equation

A semi-discrete spatial finite difference approximation to the complex Ginzburg-Landau equation with cubic non-linearity is considered. Using the fractional powers of a sectorial operator, discrete versions of the Sobolev spaces H 5, and Gevrey classes of regularityG, are introduced.Discrete versions of some standard Sobolev space norm inequalities are proved.