Finite Element Approximation for the Dynamics of Fluidic Two-Phase
Biomembranes
Biomembranes
File(s)
Accepted version
Author(s)
Barrett, JW
Garcke, H
Nürnberg, R
Type
Journal Article
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.
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.
Date Issued
2017-12-12
Date Acceptance
2017-08-14
Citation
ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN), 2017, 51 (6), pp.2319-2366
ISSN
0764-583X
Publisher
EDP Sciences
Start Page
2319
End Page
2366
Journal / Book Title
ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN)
Volume
51
Issue
6
Copyright Statement
© EDP Sciences
Identifier
http://arxiv.org/abs/1611.05343v1
Subjects
math.NA
math.NA
physics.comp-ph
Notes
61 pages, 17 figures
Publication Status
Published