This paper is concerned with the designing, analyzing and implementing linear and nonlinear discretization scheme for the distributed optimal control problem (OCP) with the Cahn-Hilliard (CH) equation as constrained. We propose three difference schemes to approximate and investigate the solution behaviour of the OCP for the CH equation. We present the convergence analysis of the proposed discretization. We verify our findings by presenting numerical experiments.

翻译：本文关注以Cahn-Hilliard（CH）方程为约束的分布型最优控制问题（OCP）的线性与非线性离散格式的设计、分析及实现。我们提出了三种差分格式来逼近并研究CH方程OCP的解行为，给出了所提离散格式的收敛性分析，并通过数值实验验证了研究结论。