Parametric FEM for geometric biomembranes Academic Article

abstract

• We consider geometric biomembranes governed by an L2-gradient flow for bending energy subject to area and volume constraints (Helfrich model). We give a concise derivation of a novel vector formulation, based on shape differential calculus, and corresponding discretization via parametric FEM using quadratic isoparametric elements and a semi-implicit Euler method. We document the performance of the new parametric FEM with a number of simulations leading to dumbbell, red blood cell and toroidal equilibrium shapes while exhibiting large deformations. 2010 Elsevier Inc.

authors

• Bonito, Andrea

published proceedings

• JOURNAL OF COMPUTATIONAL PHYSICS

author list (cited authors)

• Bonito, A., Nochetto, R. H., & Pauletti, M. S.

citation count

• 58

complete list of authors

• Bonito, Andrea||Nochetto, Ricardo H||Pauletti, M Sebastian

publication date

• January 2010

publisher

• Elsevier  Publisher

published in

• Journal of Computational Physics  Journal

keywords

• Bending Energy
• Biomembrane
• Geometric Flow
• Gradient Flow
• Helfrich
• Isoparametric Elements
• Moving Finite Elements
• Red Blood Cell
• Shape Differential Calculus
• Willmore

Digital Object Identifier (DOI)

• 10.1016/j.jcp.2009.12.036

start page

• 3171

end page

• 3188

volume

• 229

issue

• 9

URL

• http%3A%2F%2Fdx.doi.org%2F10.1016%2Fj.jcp.2009.12.036