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.
Accepté le :
DOI : 10.1051/m2an/2017037
Mots clés : Fluidic membranes, incompressible two-phase Navier–Stokes flow, parametric finite elements, Helfrich energy, spontaneous curvature, local surface area conservation, line energy, surface phase field model, surface Cahn–Hilliard equation, Marangoni-type effects
@article{M2AN_2017__51_6_2319_0,
author = {Barrett, John W. and Garcke, Harald and N\"urnberg, Robert},
title = {Finite element approximation for the dynamics of fluidic two-phase biomembranes},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {2319--2366},
publisher = {EDP-Sciences},
volume = {51},
number = {6},
year = {2017},
doi = {10.1051/m2an/2017037},
zbl = {1383.35153},
mrnumber = {3745174},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2017037/}
}
TY - JOUR AU - Barrett, John W. AU - Garcke, Harald AU - Nürnberg, Robert TI - Finite element approximation for the dynamics of fluidic two-phase biomembranes JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 2319 EP - 2366 VL - 51 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2017037/ DO - 10.1051/m2an/2017037 LA - en ID - M2AN_2017__51_6_2319_0 ER -
%0 Journal Article %A Barrett, John W. %A Garcke, Harald %A Nürnberg, Robert %T Finite element approximation for the dynamics of fluidic two-phase biomembranes %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 2319-2366 %V 51 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2017037/ %R 10.1051/m2an/2017037 %G en %F M2AN_2017__51_6_2319_0
Barrett, John W.; Garcke, Harald; Nürnberg, Robert. Finite element approximation for the dynamics of fluidic two-phase biomembranes. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 6, pp. 2319-2366. doi : 10.1051/m2an/2017037. http://www.numdam.org/articles/10.1051/m2an/2017037/
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