Finite element methods for director fields on flexible surfaces

URN to cite this document:: urn:nbn:de:bvb:355-epub-282158
DOI to cite this document:: 10.5283/epub.28215

Bartels, Sören ; Dolzmann, Georg ; Nochetto, Ricardo H. ; Raisch, Alexander

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Date of publication of this fulltext: 17 May 2013 08:10

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Abstract

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 ...