On a surface finite element method for biomembranes with lipid decomposition
Björn Stinner · 2009
Bilayers consisting of lipids molecules are the basic component of cell membranes. Vesicles formed from such biomembranes show a variety of interesting shapes that can be explained by its elastic bending energy. Due to inhomogeneities the lipids may separate and form different phases on the membrane which results in an energy contribution from the phase interfaces. We have been numerically studying equilibrium shapes, i.e., local energy minima by relaxing suitable initial shapes. A suitable (kind of) gradient flow dynamics has been defined for this purpose where the inter-membrane domains are described using the phase field methodology. The governing equations consist of pde on the membrane surface describing the phase separation coupled to a geometric evolution law for the membrane. The discretisation is based on representing the membrane by a triangulated surface on which quadratic parametric FEs are defined. The convergence as grid parameter and diffuse interface thickness tend to zero has been numerically investigated. Further issues are the sharp interface limit of the phase-field approach and adaptive mesh refinement.