Recovery Type a Posteriori Error Estimation of an Adaptive Finite Element Method for Cahn–Hilliard Equation

In this paper, we derive a novel recovery type a posteriori error estimation of the Crank–Nicolson finite element method for the Cahn–Hilliard equation. To achieve this, we employ both the elliptic reconstruction technique and a time reconstruction technique based on three time-level approximations, resulting in an optimal a posteriori error estimator. We propose a time-space adaptive algorithm that utilizes the derived a posteriori error estimator as error indicators. Numerical experiments are presented to validate the theoretical findings, including comparing with an adaptive finite element method based on a residual type a posteriori error estimator.