  We propose a robust simulation method for phospholipid membranes. It is based
on a mixed three-field formulation that accounts for tangential fluidity
(Boussinesq-Scriven law), bending elasticity (Canham-Helfrich model) and
inextensibility. The unknowns are the velocity, vector curvature and surface
pressure fields, all of which are interpolated with linear continuous finite
elements. The method is semi-implicit - it requires the solution of a single
linear system per time step. Conditional time stability is observed, with a
time step restriction that scales as the square of the mesh size. Mesh quality
and refinement are maintained by adaptively remeshing. Another ingredient is a
numerical force that emulates the action of an optical tweezer, allowing for
virtual interaction with the membrane. Extensive relaxation experiments are
reported. Comparisons to exact shapes reveal the orders of convergence for
position (5/3), vector curvature (3/2), surface pressure (1) and bending energy
(2). Tweezing experiments are also presented. Convergence to the exact dynamics
of a cylindrical tether is confirmed. Further tests illustrate the robustness
of the method (six tweezers acting simultaneously) and the significance of
viscous effects on membrane deformation under external forces.
