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In the paper the phase diagram of $J_1-J_2$ frustrated antiferromagnet withspin $S=1$ and single-ion anisotropy is studied on the planar quadratic latticein the cluster approximation. The Bogolyubov inequality is adopted for theGibbs 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 theantiferromagnetic nearest-neighbour ($J_1<0$) and next-nearest-neighbour($J_2<0$) interactions. In particular, the occurrence of tricritical and triplepoints 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 classicalMFA method, adopted here for the model in question, as well as with selectedliterature results for particular choices of interaction parameters.

Phase Diagram of the $J_1$ - $J_2$ Frustrated Anisotropic Antiferromagnet with Spin $S=1$ on the Quadratic Lattice