  In the paper the phase diagram of $J_1-J_2$ frustrated antiferromagnet with
spin $S=1$ and single-ion anisotropy is studied on the planar quadratic lattice
in the cluster approximation. The Bogolyubov inequality is adopted for the
Gibbs energy calculation for the case of $2 \times 2$ and $4 \times 4$
clusters. On this basis, the ranges of existence of the anfiferromagnetic,
superantiferromagnetic and paramagnetic phases are investigated for the
antiferromagnetic nearest-neighbour ($J_1<0$) and next-nearest-neighbour
($J_2<0$) interactions. In particular, the occurrence of tricritical and triple
points is discussed and a comparison between the results for $2 \times 2$ and
$4 \times 4$ clusters is made. The results are also compared with the classical
MFA method, adopted here for the model in question, as well as with selected
literature results for particular choices of interaction parameters.
