Geodesic
Finite element methods for director fields on flexible surfaces
Sören Bartels1 orcid ; Georg Dolzmann2 ; Ricardo H. Nochetto3 orcid ; Alexander Raisch1
1Universität Bonn, Germany
2Universität Regensburg, Germany
3University of Maryland, College Park, USA
Interfaces and free boundaries, Tome 14 (2012) no. 2, pp. 231-272

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DOI

We introduce a nonlinear model for the evolution of biomembranes driven by the L2-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.
DOI : 10.4171/ifb/281
Classification : 35-XX, 74-XX, 00-XX
Mots-clés : Finite elements, surfaces, biomembranes, surfactants, director fields

Sören Bartels  1   ; Georg Dolzmann  2   ; Ricardo H. Nochetto  3   ; Alexander Raisch  1

1 Universität Bonn, Germany
2 Universität Regensburg, Germany
3 University of Maryland, College Park, USA 
Sören Bartels; Georg Dolzmann; Ricardo H. Nochetto; Alexander Raisch. Finite element methods for director fields on flexible surfaces. Interfaces and free boundaries, Tome 14 (2012) no. 2, pp. 231-272. doi: 10.4171/ifb/281
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     title = {Finite element methods for director fields on flexible surfaces},
     journal = {Interfaces and free boundaries},
     pages = {231--272},
     year = {2012},
     volume = {14},
     number = {2},
     doi = {10.4171/ifb/281},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/281/}
}
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