  The development of parallel supercomputers allows today the detailed study of
the collapse and the fragmentation of prestellar cores with increasingly
accurate numerical simulations. Thanks to the advances in sub-millimeter
observations, a wide range of observed initial conditions enable us to study
the different modes of low-mass star formation. The challenge for the
simulations is to reproduce the observational results. Two main numerical
methods, namely AMR and SPH, are widely used to simulate the collapse and the
fragmentation of prestellar cores. We compare thoroughly these two methods
within their standard framework. We use the AMR code RAMSES and the SPH code
DRAGON. Our physical model is as simple as possible and consists of an
isothermal sphere rotating around the z-axis. We first study the conservation
of angular momentum as a function of the resolution. Then, we explore a wide
range of simulation parameters to study the fragmentation of prestellar cores.
There seems to be a convergence between the two methods, provided resolution in
each case is sufficient. Resolution criteria adapted to our physical cases, in
terms of resolution per Jeans mass, for an accurate description of the
formation of protostellar cores are deduced from the present study. This
convergence is encouraging for future work in simulations of low-mass star
formation, providing the aforementioned criteria are fulfilled.
  Higher resolution figures can be downloaded at
http://www-dapnia.cea.fr/Projets/COAST/paper_amrvssph.pdf
