We consider geometric biomembranes governed by an L^2-gradient flow for bending energy subject to area and volume constraints (Helfrich model). We give a concise derivation of a novel vector formulation, based on shape differential calculus, and corresponding discretization via parametric FEM using quadratic isoparametric elements and a semi-implicit Euler method. We document the performance of the new parametric FEM with a number of simulations leading to dumbbell, red blood cell and toroidal equilibrium shapes while exhibiting large deformations.
['Andrea Bonito', 'Ricardo H. Nochetto', 'M. Sebastian Pauletti']
Parametric FEM for geometric biomembranes