Solution of the Optimal Control Problem for the Cahn-Hilliard Equation Using Finite Difference Approximation

TL;DR

This paper develops and analyzes finite difference schemes for solving the optimal control problem constrained by the Cahn-Hilliard equation, including convergence proofs and numerical validation.

Contribution

It introduces three new difference schemes for discretizing the OCP with the Cahn-Hilliard equation and provides their convergence analysis.

Findings

Proposed three difference schemes for the OCP with CH equation

Established convergence of the discretization methods

Validated results through numerical experiments

Abstract

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.