TY - JOUR
T1 - Approximation of the Long-Time Dynamics of the Dynamical System Generated by the Ginzburg-Landau Equation
AU - Tone , Cristina
AU - Tone , Florentina
JO - Communications in Mathematical Research 
VL - 4
SP - 501
EP - 522
PY - 2023
DA - 2023/11
SN - 39
DO - http://doi.org/10.4208/cmr.2023-0003
UR - https://global-sci.org/intro/article_detail/cmr/22098.html
KW - Ginzburg-Landau equation, implicit Euler scheme, long-time stability, attractors.
AB - <p style="text-align: justify;">In this article we consider the (complex) Ginzburg-Landau equation, we discretize in time using the implicit Euler scheme, and with the aid of
the discrete Gronwall lemma and of the discrete uniform Gronwall lemma we
prove that the global attractors generated by the numerical scheme converge to
the global attractor of the continuous system as the time-step approaches zero.</p>