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VOL. 17 | 2016 New Advances in the Study of Generalized Willmore Surfaces and Flow
Bhagya Athukorallage, Eugenio Aulisa, Giorgio Bornia, Thanuja Paragoda, Magdalena Toda

Editor(s) Ivaïlo M. Mladenov, Guowu Meng, Akira Yoshioka


In this paper we study a Generalized Willmore flow for graphs and its numerical applications.

First, we derive the time dependent equation which describes the geometric evolution of a Generalized Willmore flow in the graph case. This equation is recast in divergence form as a coupled system of second order nonlinear PDEs.

Furthermore, we study finite element numerical solutions for steady-state cases obtained with the help of the FEMuS library (Finite Element Multiphysics Solver). We use automatic differentiation (AD) tools to compute the exact Jacobian of the coupled PDE system subject to Dirichlet boundary conditions.


Published: 1 January 2016
First available in Project Euclid: 15 December 2015

zbMATH: 1345.35125
MathSciNet: MR3445427

Digital Object Identifier: 10.7546/giq-17-2016-133-142

Rights: Copyright © 2016 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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