An efficient data assimilation based unconditionally stable scheme for Cahn–Hilliard equation

This paper aims to present an efficient numerical method for solving the Cahn–Hilliard equation incorporating a data assimilation term. The data assimilation term employs a feedback control strategy to guide the computational solution towards the observed data. The Crank–Nicolson formula is employed for discretizing the equation system, while a scalar auxiliary variable approach is adopted to ensure energy dissipation preservation. The proposed scheme attains second-order accuracy in both temporal and spatial dimensions. The unconditional energy stability of the scheme is proven theoretically. Numerous numerical experiments are conducted to illustrate the efficacy of the proposed scheme.