  Doppler imaging (DI) is a powerful spectroscopic inversion technique that
enables conversion of a line profile time series into a two-dimensional map of
the stellar surface inhomogeneities. In this paper we investigate the accuracy
of chemical abundance DI of Ap/Bp stars and assess the impact of several
different systematic errors on the reconstructed spot maps. We simulate
spectroscopic observational data for different spot distributions in the
presence of a moderately strong dipolar magnetic field. We then reconstruct
chemical maps using different sets of spectral lines and making different
assumptions about line formation in the inversion calculations. Our numerical
experiments demonstrate that a modern DI code successfully recovers the input
chemical spot distributions comprised of multiple circular spots at different
latitudes or an element overabundance belt at the magnetic equator. For the
optimal reconstruction the average reconstruction errors do not exceed ~0.10
dex. The errors increase to about 0.15 dex when abundance distributions are
recovered from a few and/or blended spectral lines. Ignoring a 2.5 kG dipolar
magnetic field in chemical abundance DI leads to an average relative error of
0.2 dex and maximum errors of 0.3 dex. Similar errors are encountered if a DI
inversion is carried out neglecting a non-uniform continuum brightness
distribution and variation of the local atmospheric structure. This series of
numerical DI simulations proves that inversions with simplifying assumptions of
the non-magnetic radiative transfer and a single model atmosphere are generally
reliable. We assess magnetic field strengths of several dozen Ap/Bp stars
previously studied with DI methods, concluding that the vast majority of the
published chemical spot maps are unaffected by the systematic errors addressed
in this paper. (Abridged)
