Gradient flow dynamics of two-phase biomembranes: Sharp interface variational formulation and finite element approximation
File(s)
Published version
Author(s)
Barrett, John W
Garcke, Harald
Nürnberg, Robert
Type
Journal Article
Abstract
A finite element method for the evolution of a two-phase membrane in a sharp interfaceformulation is introduced. The evolution equations are given as anL2–gradient flow of an energy involvingan elastic bending energy and a line energy. In the two phases Helfrich-type evolution equations are prescribed,and on the interface, an evolving curve on an evolving surface, highly nonlinear boundary conditions have tohold. Here we consider bothC0– andC1–matching conditions for the surface at the interface. A new weakformulation is introduced, allowing for a stable semidiscrete parametric finite element approximation of thegoverning equations. In addition, we show existence and uniqueness for a fully discrete version of the scheme.Numerical simulations demonstrate that the approach can deal with a multitude of geometries. In particular,the paper shows the first computations based on a sharp interface description, which are not restricted tothe axisymmetric case.
Date Issued
2018-01-31
Date Acceptance
2018-01-18
Citation
SMAI Journal of Computational Mathematics, 2018, 4, pp.151-195
ISSN
2426-8399
Publisher
SMAI-JCM
Start Page
151
End Page
195
Journal / Book Title
SMAI Journal of Computational Mathematics
Volume
4
Copyright Statement
©Société de Mathématiques Appliquées et Industrielles, 2018Certainsdroits réservés. Published open access under a CC-BY-NC-ND (https://creativecommons.org/licenses/by-nc-nd/3.0/)
Identifier
http://arxiv.org/abs/1706.09631v1
Subjects
math.NA
math.NA
physics.comp-ph
35R01, 49Q10, 65M12, 65M60, 82B26, 92C10
Notes
55 pages, 22 figures
Publication Status
Published