Special Session 2: Nonlinear evolution PDEs and interfaces in applied sciences
In two-phase flow the interface often has important additional aspects. First we discuss
the Boussinesq-Scriven surface fluid model and a model for biomembranes
due to Arroyo and DeSimone taking curvature elasticity forcing into account.
We then present analytical properties of the model and introduce a
parametric finite element method for the evolution problem. For the
discrete equations we show stability estimates and finally we present
numerical computations in two and three space dimensions which show different
phenomena stemming from surface viscosity and from forces originating from the Helfrich energy.