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 $.
Citation: Narcisse Batangouna. A robust family of exponential attractors for a time semi-discretization of the Ginzburg-Landau equation[J]. AIMS Mathematics, 2022, 7(1): 1399-1415. doi: 10.3934/math.2022082
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 $.
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Narcisse Batangouna. A robust family of exponential attractors for a time semi-discretization of the Ginzburg-Landau equation[J]. AIMS Mathematics, 2022, 7(1): 1399-1415. doi: 10.3934/math.2022082
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