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

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 C-1 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.(C) 2021 Elsevier B.V. All rights reserved.