Finite Element Approximation for the Dynamics of Fluidic Two-Phase Biomembranes
arXiv:1611.05343 · doi:10.1051/m2an/2017037
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.
61 pages, 17 figures
References in corpus (5)
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Cited by in corpus (7)
- Parametric finite element approximations of curvature driven interface evolutions
- Numerical modelling of phase separation on dynamic surfaces
- Numerical approximation of curve evolutions in Riemannian manifolds
- Swinging and tumbling of multicomponent vesicles in flow
- A fully discrete evolving surface finite element method for the Cahn-Hilliard equation with a regular potential
- Structure preserving discretisations of gradient flows for axisymmetric two-phase biomembranes
- A parametric finite element method for the incompressible Navier--Stokes equations on an evolving surface