  We investigate the gravitational fragmentation of expanding shells in the
context of the linear thin--shell analysis. We make use of two very different
numerical schemes; the FLASH Adaptive Mesh Refinement code and a version of the
Benz Smoothed Particle Hydrodynamics code. We find that the agreement between
the two codes is excellent. We use our numerical results to test the
thin--shell approximation and we find that the external pressure applied to the
shell has a strong effect on the fragmentation process. In cases where shells
are not pressure--confined, the shells thicken as they expand and hydrodynamic
flows perpendicular to the plane of the shell suppress fragmentation at short
wavelengths. If the shells are pressure--confined internally and externally, so
that their thickness remains approximately constant during their expansion, the
agreement with the analytical solution is better.
