Finite Element Simulation of Biological Viscous Membranes

Abstract

In this work we study the dynamical behavior of biological membranes subject to area and volume constraints. The membrane is discretized by a surface mesh made of linear or quadratic triangular elements whose nodes are explicitly updated at each time step. The Stokes operator on the surface is solved using linear or quadratic elements for velocity and membrane pressure with stabilization by pressure gradient projection. The volume constraint is treated by adding an internal pressure. The membrane curvature is computed either by using Meyer’s method or the Laplace-Beltrami identity and both methods compared. The different ingredients present in our formulation are detailed throughout the work
and presented together with examples in three spatial dimensions.