Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions

In this paper, we study the three-dimensional deformation of a vesicle membrane under the elastic bending energy, with prescribed bulk volume and surface area. Both static and dynamic deformations are considered. A newly developed energetic variational formulation is employed to give an effective Eulerian description. Efficient time and spatial discretizations are considered and implemented. Numerical experiments illustrate some fascinating phenomena that are of interests in real applications.