A robust family of exponential attractors for a time semi-discretization of the Ginzburg-Landau equation

We consider a time semidiscretization of the Ginzburg-Landau equation by the backward Euler scheme. For each time step tau, we build an exponential attractor of the dynamical system associated to the scheme. We prove that, as tau tends to 0, this attractor converges for the symmetric Hausdorff distance to an exponential attractor of the dynamical system associated to the Allen-Cahn equation. We also prove that the fractal dimension of the exponential attractor and of the global attractor is bounded by a constant independent of tau.

Automated summary

In this article, we study the time semidiscretization of the Ginzburg-Landau equation using the backward Euler scheme. We construct an exponential attractor for the dynamical system associated with each time step tau. We prove that as tau approaches 0, this attractor converges to the exponential attractor of the dynamical system associated with the Allen-Cahn equation, and also show that the fractal dimension of the attractor and the global attractor is bounded by a constant independent of tau.