Finite element methods for director fields on flexible surfaces

  • Sören Bartels

    Universität Bonn, Germany
  • Georg Dolzmann

    Universität Regensburg, Germany
  • Ricardo H. Nochetto

    University of Maryland, College Park, USA
  • Alexander Raisch

    Universität Bonn, Germany


We introduce a nonlinear model for the evolution of biomembranes driven by the -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.

Cite this article

Sören Bartels, Georg Dolzmann, Ricardo H. Nochetto, Alexander Raisch, Finite element methods for director fields on flexible surfaces. Interfaces Free Bound. 14 (2012), no. 2, pp. 231–272

DOI 10.4171/IFB/281