Parametric FEM for geometric biomembranes
We consider geometric biomembranes governed by an L2 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.
biomembrane bending energy helfrich shape differential calculus isoparametric elements red blood cell moving finite elements geometric flow gradient flow willmore