  Embedded planets disturb the density structure of the ambient disk and
gravitational back-reaction will induce possibly a change in the planet's
orbital elements. The accurate determination of the forces acting on the planet
requires careful numerical analysis. Recently, the validity of the often used
fast orbital advection algorithm (FARGO) has been put into question, and
special numerical resolution and stability requirements have been suggested. In
this paper we study the process of planet-disk interaction for small mass
planets of a few Earth masses, and reanalyze the numerical requirements to
obtain converged and stable results. One focus lies on the applicability of the
FARGO-algorithm. Additionally, we study the difference of two and
three-dimensional simulations, compare global with local setups, as well as
isothermal and adiabatic conditions. We study the influence of the planet on
the disk through two- and three-dimensional hydrodynamical simulations. To
strengthen our conclusions we perform a detailed numerical comparison where
several upwind and Riemann-solver based codes are used with and without the
FARGO-algorithm.
  With respect to the wake structure and the torque density acting on the
planet we demonstrate that the FARGO-algorithm yields correct results, and that
at a fraction of the regular cpu-time. We find that the resolution requirements
for achieving convergent results in unshocked regions are rather modest and
depend on the pressure scale height of the disk. By comparing the torque
densities of 2D and 3D simulations we show that a suitable vertical averaging
procedure for the force gives an excellent agreement between the two. We show
that isothermal and adiabatic runs can differ considerably, even for adiabatic
indices very close to unity.
