Geodesic
Finite element approximation for the dynamics of fluidic two-phase biomembranes
Barrett, John W.1 ; Garcke, Harald2  ; Nürnberg, Robert1 
1 Department of Mathematics, Imperial College, London, SW7 2AZ, U.K.
2 Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 6, pp. 2319-2366

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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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DOI : 10.1051/m2an/2017037
Classification : 35Q35, 65M12, 65M60, 76D05, 76D27, 76M10, 76Z99, 92C05
Keywords: 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

Barrett, John W. 1 ; Garcke, Harald 2 ; Nürnberg, Robert 1

1 Department of Mathematics, Imperial College, London, SW7 2AZ, U.K.
2 Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany. 
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     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},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2017037/}
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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

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