  We consider surface finite elements and a semi-implicit time stepping scheme
to simulate fluid deformable surfaces. Such surfaces are modeled by
incompressible surface Navier-Stokes equations with bending forces. Here, we
consider closed surfaces and enforce conservation of the enclosed volume. The
numerical approach builds on higher order surface parameterizations, a
Taylor-Hood element for the surface Navier-Stokes part, appropriate
approximations of the geometric quantities of the surface mesh redistribution
and a Lagrange multiplier for the constraint. The considered computational
examples highlight the solid-fluid duality of fluid deformable surfaces and
demonstrate convergence properties that are known to be optimal for different
sub-problems.
