A C1 finite element method for axisymmetric lipid membranes in the presence of the Gaussian energy

• Published in: Computer methods in applied mechanics and engineering 2022-03, Vol.391, p.1, Article 114472
• Main Author: Ebrahimi, Faezeh
• Format: Article
• Language: English
• Subjects: [formula omitted] Argyris finite element; Finite element method; Gaussian curvature; Lipid membranes; Lipids; Mathematical models; Membranes; Phase field model; Topology; Topology changes
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2021.114472

The classical model of lipid membranes is expressed in terms of a curvature-dependent energy involving the mean and the Gaussian curvatures of membranes. It is customary to ignore the Gaussian energy as it takes a constant value for topologically equivalent closed membranes. In this work, we study the effect of the Gaussian energy on configurations of axisymmetric lipid membranes by using a phase field model. As the weak form of the governing equations involves the second-order derivatives of the phase field function, we employ C1 Argyris finite element to approximate solutions. The numerical results of this paper suggest that including the Gaussian energy in the existing mathematical model may be necessary to capture the topology changes of membranes accurately. •Gaussian energy affects the phase transition of closed membranes.•Conforming C1 finite element is effective to accurately model lipid membranes.•Gaussian curvature is necessary for accurately capturing the topology changes of closed membranes.