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arXiv · 1611.05343

Finite Element Approximation for the Dynamics of Fluidic Two-Phase Biomembranes

John W. Barrett·Harald Garcke·Robert Nürnberg
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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.

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John W. Barrett, Harald Garcke, Robert Nürnberg. 2016-11-16. Finite Element Approximation for the Dynamics of Fluidic Two-Phase Biomembranes. https://doi.org/10.1051/m2an%2F2017037

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