Second-order finite element scheme of the viscous Cahn–Hilliard equation with energy-stable method

In this paper, we develop and analyze a fully discrete numerical scheme for the viscous Cahn–Hilliard equation. To enhance the stability of the scheme and allow for larger time steps, we introduce two artificial stabilization terms. We derive the scheme and rigorously prove, through error analysis, that it achieves second-order accuracy in both space and time. Numerical examples are provided to demonstrate the efficiency of the proposed method.