Decoupled energy stable schemes for phase-field vesicle membrane model

We consider the numerical approximations of the classical phase-field vesicle membrane models proposed a decade ago in Du et al. (2004) 6. We first reformulate the model derived from an energetic variational formulation into a form which is suitable for numerical approximation, and establish the energy dissipation law. Then, we develop a stabilized, decoupled, time discretization scheme for the coupled nonlinear system. The scheme is unconditionally energy stable and leads to linear and decoupled elliptic equations to be solved at each time step. Stability analysis and ample numerical simulations are presented thereafter.