Error estimates for approximations of a gradient dynamics for phase field elastic bending energy of vesicle membrane deformation
Liyong Zhu, Qiang Du · Mathematical Methods in the Applied Sciences · 2013
In this paper, we study the numerical approximations of a gradient flow associated with a phase field bending elasticity model of a vesicle membrane with prescribed volume and surface area. A spatially semi-discrete scheme based on a mixed finite element formulation and a fully discrete in space and time scheme are analyzed. Optimal order error estimates are rigorously derived for these numerical schemes without any a priori assumption. Copyright © 2013 John Wiley & Sons, Ltd.