  Accuracy in complex dielectric permittivity calculations in binary dielectric
mixtures in two-dimensions are reported by taking into account the shape of the
inclusion phase. The dielectric permittivity of the mixtures were calculated
using the finite element, and the permittivities were estimated by two
different procedures. The results were compared with those of analytical models
based on mean field approximation and regular arrangement of disks. We have
approached the problem emphasizing the finite-size behavior in which regular
polygons with $n$ sides were assumed to mimic the disk inclusion phase. It was
found that at low concentrations, $< 30 %$, considering an decagon ($n=10$)
cause an error of $<0.1 %$ in the effective medium quantities compared with the
results obtained using the analytical models.
