Finite Element Approximation for the Dynamics of Fluidic Two-Phase Biomembranes
Numerical Analysis
2019-11-01 v1 Computational Physics
Abstract
Biomembranes and vesicles consisting of multiple phases can attain a multitude of shapes, undergoing complex shape transitions. We study a Cahn--Hilliard model on an evolving hypersurface coupled to Navier--Stokes equations on the surface and in the surrounding medium to model these phenomena. The evolution is driven by a curvature energy, modelling the elasticity of the membrane, and by a Cahn--Hilliard type energy, modelling line energy effects. A stable semidiscrete finite element approximation is introduced and, with the help of a fully discrete method, several phenomena occurring for two-phase membranes are computed.
Keywords
Cite
@article{arxiv.1611.05343,
title = {Finite Element Approximation for the Dynamics of Fluidic Two-Phase Biomembranes},
author = {John W. Barrett and Harald Garcke and Robert Nürnberg},
journal= {arXiv preprint arXiv:1611.05343},
year = {2019}
}
Comments
61 pages, 17 figures