Finite element approximation for the dynamics of fluidic two-phase biomembranes. (English) Zbl 1383.35153
Summary: 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.
MSC:
35Q35 | PDEs in connection with fluid mechanics |
65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
76D05 | Navier-Stokes equations for incompressible viscous fluids |
76D27 | Other free boundary flows; Hele-Shaw flows |
76M10 | Finite element methods applied to problems in fluid mechanics |
76Z99 | Biological fluid mechanics |
92C05 | Biophysics |