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Finite element approximation for the dynamics of asymmetric fluidic biomembranes

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Title: Finite element approximation for the dynamics of asymmetric fluidic biomembranes
Authors: Barrett, JW
Garcke, H
Nurnberg, R
Item Type: Journal Article
Abstract: We present a parametric finite element approximation of a fluidic membrane, whose evolution is governed by a surface Navier–Stokes equation coupled to bulk Navier–Stokes equations. The elastic properties of the membrane are modelled with the help of curvature energies of Willmore and Helfrich type. Forces stemming from these energies act on the surface fluid, together with a forcing from the bulk fluid. Using ideas from PDE constrained optimization, a weak formulation is derived, which allows for a stable semi-discretization. An important new feature of the present work is that we are able to also deal with spontaneous curvature and an area difference elasticity contribution in the curvature energy. This allows for the modelling of asymmetric membranes, which compared to the symmetric case lead to quite different shapes. This is demonstrated in the numerical computations presented.
Issue Date: 18-Aug-2016
Date of Acceptance: 26-Mar-2016
URI: http://hdl.handle.net/10044/1/30439
DOI: https://dx.doi.org/10.1090/mcom/3162
ISSN: 1088-6842
Publisher: American Mathematical Society
Start Page: 1037
End Page: 1069
Journal / Book Title: Mathematics of Computation
Volume: 86
Copyright Statement: © Copyright 2016 American Mathematical Society
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
NAVIER-STOKES EQUATIONS
RED-BLOOD-CELLS
PARAMETRIC APPROXIMATION
WILLMORE FLOW
VESICLES
SHAPE
DISCRETIZATION
CURVATURE
MEMBRANES
SURFACES
0102 Applied Mathematics
0103 Numerical And Computational Mathematics
0802 Computation Theory And Mathematics
Numerical & Computational Mathematics
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences