Adaptive Finite Element Method for a Phase Field Bending Elasticity Model of Vesicle Membrane Deformations

In this paper, a three-dimensional adaptive finite element method is developed for a variational phase field bending elasticity model of vesicle membrane deformations. Using a mixed finite element formulation, residual type a posteriori error estimates are derived for the associated nonlinear system of equations and, they are used to introduce the mesh refinement and coarsening. The resulting mesh adaptivity significantly improves the efficiency of the phase field simulation of vesicle membranes and enhances its capability in handling complex shape and topological changes. The effectiveness of the adaptive method is further demonstrated through numerical examples.