Fully implicit methodology for the dynamics of biomembranes and capillary interfaces by combining the level set and Newton methods

- Finite Element method tailored for the simulation of individual biomembranes and capillary interfaces in a Newtonian fluid.
- Fully implicit time scheme to overcome instability issues related to the explicit treatment of the highly non-linear force.
- Inexact Newton strategies with second-order convergence behavior to solve the capillary and vesicle problems.
- Significantly larger time step sizes with respect to the explicit method are allowed.