A filament of an incompressible highly viscous fluid that is supported at its ends sags
under the influence of gravity. Its instantaneous shape resembles that of a catenary,
but evolves with time. At short times, the shape is dominated by bending deformations.
At intermediate times, the effects of stretching become dominant everywhere except
near the clamping boundaries where bending boundary layers persist. Finally, the
filament breaks off in finite time via strain localization and pinch-off.