  The growing tensions between the early Universe and the late Universe
increasingly highlight the importance of developing precise probes for late
cosmology. As significant late-Universe probes, Type Ia supernovae (SNe Ia) and
gravitational waves (GWs) can provide measurements of relative and absolute
distances, respectively. Their complementary nature is likely to break the
degeneracies among cosmological parameters, thereby yielding more precise
constraints. In this study, we use 43 gravitational-wave sources from the Third
LIGO-Virgo-KAGRA Gravitational-Wave Transient Catalog (GWTC-3) and 1590 SNe Ia
from Pantheon+ compilation to constrain the dark energy models, as an attempt
to achieve precise late-Universe cosmological constraints. For the dark siren
GW event, we estimate the corresponding redshift using the binary black hole
redshift distribution model. The combination of GW and SNe Ia data could
provide the precision on the Hubble constant (H0) and the present matter
density (Omega_m) of approximately 20% and 8% for the LambdaCDM model. If we
consider the equation of state of dark energy (w), the combination sample
constrains the precision of w to approximately 30%. Although the combination of
GW and SNe Ia observations effectively breaks degeneracies among various
cosmological parameters, yielding more stringent constraints, the precision of
these constraints still does not meet the stringent standards required by
precision cosmology. However, it is reasonable to anticipate that, in the near
future, the joint observations of GWs and SNe Ia will become a powerful tool,
particularly in the late Universe, for the precise measurement of cosmological
parameters.
