2023/08/23 by Dieunel Dor, Dor, Dieunel, Morgan Pierre +1 · 1 citation
Computer Science · Engineering · Materials Science · #37L30 #65M12 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical Analysis (math.NA) #Solidification and crystal growth phenomena #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2308.12164
openalex publication_date 2023/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a linear implicit-explicit (IMEX) time discretization of the Cahn-Hilliard equation with a source term, endowed with Dirichlet boundary conditions. For every time step small enough, we build an exponential attractor of the discrete-in-time dynamical system associated to the discretization. We prove that, as the time step tends to 0, this attractor converges for the symmmetric Hausdorff distance to an exponential attractor of the continuous-in-time dynamical system associated with the PDE. We also prove that the fractal dimension of the exponential attractor (and consequently, of the global attractor) is bounded by a constant independent of the time step. The results also apply to the classical Cahn-Hilliard equation with Neumann boundary conditions.