A Nitsche-type variational formulation for the shape deformation of a single component vesicle

This paper concerns the development of a finite-element formulation using Nitsche’ method for the phase-field model to capture an equilibrium shape of a single component vesicle. The phase-field model derived from the minimization of the curvature energy results in a nonlinear fourth-order partial differential equation. A standard conforming Galerkin formulation thus requires C¹-elements. We derive a nonconforming finite-element formulation that can be applied to C⁰-elements and prove its consistency. Continuity of the first derivatives across interelement boundaries is weakly imposed and stabilization of the method is achieved via Nitsche's method. The capability of the proposed finite-element formulation is demonstrated through numerical study of the equilibrium shapes of axisymmetric single component vesicles along with budding and fission phenomena.