Numerical analysis of finite element method for time‐fractional Cahn‐Hilliard‐Cook equation

Abstract

In this paper, we propose a Galerkin finite element method for the Cahn‐Hilliard‐Cook equation involving the Caputo‐type fractional derivative, which can be used to describe the interface phenomena for modeling the phase transitions with the random effects and the properties of shape memory. The regularity properties of mild solution to the given problem are presented, and a result concerning the convergence error estimate of the corresponding semidiscrete scheme is established. Finally, we construct the fully discrete scheme based on the approximations of the Mittag‐Leffler function, and the strong convergence error estimate of the proposed scheme is also studied.