An Energy Stable Finite Element Scheme for the Three-Component Cahn–Hilliard-Type Model for Macromolecular Microsphere Composite Hydrogels

In this article, we present and analyze a finite element numerical scheme for three-component macromolecular microsphere composite (MMC) hydrogel model, which takes the form of ternary Cahn–Hilliard-type equation with Flory–Huggins–deGennes energy potential. The approach is based on convex–concave decomposition functional in multi-phase space, logarithmic nonlinear surface diffusion terms are treated implicitly, while concave expansive linear explicitly updated. A mass lumped spatial approximation applied, to ensure positivity phase variables. turn, positivity-preserving property can be theoretically justified proposed fully discrete scheme. addition, unconditional stability established as well, comes from convexity analysis. Several simulations carried out verify accuracy