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.

翻译：我们考虑带有Dirichlet边界条件的含源项Cahn-Hilliard方程的线性隐式-显式(IMEX)时间离散格式。对于足够小时步长，我们构造了与离散格式相关的离散时间动力系统的指数吸引子。证明当时间步长趋于0时，该吸引子在对称Hausdorff距离意义下收敛于连续时间偏微分方程动力系统的指数吸引子。同时证明该指数吸引子（进而全局吸引子）的分形维数具有独立于时间步长的常数上界。该结果同样适用于带Neumann边界条件的经典Cahn-Hilliard方程。