| Abstract: |
| We consider a space semidiscretization of the Allen-Cahn equation by conforming Lagrange finite elements. We build a family of exponential attractors associated to the discretized equations which is robust as the mesh parameter $h$ tends to $0$. As a consequence, we obtain an upper bound on the fractal dimension of the global attractor which is independent of $h$. Our proof is adapted from the result of Efendiev, Miranville and Zelik concerning the continuity of exponential attractors under perturbation of the underlying semigroup. Here, for the first time, the perturbation is a space discretization. We will also discuss the case of a time discretization and some perspectives. |
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