TY - JOUR
T1 - A Scalar Auxiliary Variable (SAV) Finite Element Numerical Scheme for the Cahn-Hilliard-Hele-Shaw System with Dynamic Boundary Conditions
AU - Yao , Changhui
AU - Zhang , Fengdan
AU - Wang , Cheng
JO - Journal of Computational Mathematics
VL - 2
SP - 544
EP - 569
PY - 2024
DA - 2024/01
SN - 42
DO - http://doi.org/10.4208/jcm.2205-m2021-0234
UR - https://global-sci.org/intro/article_detail/jcm/22891.html
KW - Cahn-Hilliard-Hele-Shaw system, Dynamic boundary conditions, Bulk energy
and surface energy, Scalar auxiliary variable formulation, Energy stability, Convergence analysis.
AB - <p style="text-align: justify;">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 important
roles. The scalar auxiliary variable approach is introduced for the physical system; the mass
conservation and energy dissipation is proved for the CHHS system. Subsequently, a fully
discrete SAV finite element scheme is proposed, with the mass conservation and energy
dissipation laws established at a theoretical level. In addition, the convergence analysis
and error estimate is provided for the proposed SAV numerical scheme.</p>