A Scalar Auxiliary Variable (SAV) Finite Element Numerical Scheme for the Cahn-Hilliard-Hele-Shaw System with Dynamic Boundary Conditions (Journal of Computational Mathematics, 2024)
In this paper, we consider the Cahn-Hilliard-Hele-Shaw (CHHS) system with the dynamic boundary conditions, in which both the bulk and surface energy parts play importantroles. The scalar auxiliary variable approach is introduced for the physical system; the massconservation and energy dissipation is proved for the CHHS system. Subsequently, a fullydiscrete SAV finite element scheme is proposed, with the mass conservation and energydissipation laws established at a theoretical level. In addition, the convergence analysisand error estimate is provided for the proposed SAV numerical scheme.