Approximation of the Long-Time Dynamics of the Dynamical System Generated by the Ginzburg-Landau Equation (Communications in Mathematical Research, 2023)
In this article we consider the (complex) Ginzburg-Landau equation, we discretize in time using the implicit Euler scheme, and with the aid ofthe discrete Gronwall lemma and of the discrete uniform Gronwall lemma weprove that the global attractors generated by the numerical scheme converge tothe global attractor of the continuous system as the time-step approaches zero.
Keywords: Ginzburg-Landau equation; implicit Euler scheme; long-time stability; attractors.