  We study numerically the reflectivity of three-dimensional (3D) photonic
crystals with a complete 3D photonic band gap, with the aim to interpret recent
experiments. We employ the finite element method to study crystals with the
cubic diamond-like inverse woodpile structure. The high-index backbone has a
dielectric function similar to silicon. We study crystals with a range of
thicknesses up to ten unit cells ($L \leq 10 c$). The crystals are surrounded
by vacuum, and have a finite support as in experiments. The
polarization-resolved reflectivity spectra reveal Fabry-P{\'e}rot fringes
related to standing waves in the finite crystal, as well as broad stop bands
with nearly $100~\%$ reflectivity, even for thin crystals. From the strong
reflectivity peaks, it is inferred that the maximum reflectivity observed in
experiments is not limited by finite size. The frequency ranges of the stop
bands are in excellent agreement with stop gaps in the photonic band structure,
that pertain to infinite and perfect crystals. The frequency ranges of the
observed stop bands hardly change with angle of incidence, which is plausible
since the stop bands are part of the 3D band gap. Moreover, this result
supports the previous assertion that intense reflection peaks measured with a
large numerical aperture provide a faithful signature of the 3D photonic band
gap. The Bragg attenuation lengths $L_{B}$ exceed the earlier estimates based
on the width of the stop band by a factor $6$ to $9$. Hence crystals with a
thickness of $12$ unit cells studied in experiments are in the thick crystal
limit ($L >> L_{B}$). In our calculations for p-polarized waves, we also
observe an intriguing hybridization of the zero reflection of Fabry-P{\'e}rot
fringes and the Brewster angle, which has not yet been observed in experiments.
