Surface finite elements for membranes with lateral phase separation
Björn Stinner · 2011
We consider vesicles formed by lipid bilayers with intra-membrane phase interfaces. A gradient flow dynamics to compute equilibrium shapes has been defined coupling a geometric evolution law for the membrane hypersurface to a surface Allen-Cahn equation for the interfaces. The discretization is based on H1 conforming quadratic isoparametric surface finite elements and a semi-implicit time discretization. Issues are the sharp interface limit, grid regularity, adaptive mesh refinement, and the influence of various physical parameters.