Bartels, Soeren and Dolzmann, Georg and Nochetto, Ricardo H. and Raisch, Alexander (2012) Finite element methods for director fields on flexible surfaces. INTERFACES AND FREE BOUNDARIES, 14 (2). pp. 231-272. ISSN 1463-9963,
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We introduce a nonlinear model for the evolution of biomembranes driven by the L-2-gradient flow of a novel elasticity functional describing the interaction of a director field on a membrane with its curvature. In the linearized setting of a graph we present a practical finite element method (FEM), and prove a priori estimates. We derive the relaxation dynamics for the nonlinear model on closed surfaces and introduce a parametric FEM. We present numerical experiments for both linear and nonlinear models, which agree well with the expected behavior in simple situations and allow predictions beyond theory.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ELASTIC PROPERTIES; WILLMORE FLOW; MEMBRANES; BILAYERS; ENERGY; PHASE; MODEL; CONFIGURATIONS; APPROXIMATION; ALGORITHM; Finite elements; surfaces; biomembranes; surfactants; director fields |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Georg Dolzmann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 25 May 2020 10:48 |
| Last Modified: | 25 May 2020 10:48 |
| URI: | https://pred.uni-regensburg.de/id/eprint/19450 |
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