  Hydrodynamics merged with single-freeze-out statistical hadronization is used
to describe the midrapidity hadron production in relativistic heavy-ion
collisions at the highest RHIC energies and to make predictions for the LHC.
Thermodynamic properties of the quark-gluon plasma are taken from lattice
simulations, at low temperatures the hadron-gas equation of state is used,
while in the cross-over region an interpolation between the two equations of
state is constructed. The initial condition for hydrodynamics is obtained from
a Glauber profile for the entropy, with the initial central temperature Ti. The
conditions obtained from the hydrodynamic expansion at the freeze-out
temperature Tf are used as input for the thermal event generator THERMINATOR.
Basic physical observables are obtained: the transverse-momentum spectra, the
elliptic flow coefficient v2, and the HBT radii. The femtoscopic observables
are evaluated with the help of the two-particle method which accounts for the
resonance decays and Coulomb final-state interactions. The problem of a
simultaneous description of all discussed observables is addressed, with the
conclusion that at the highest RHIC energies our approach gives a quite
satisfactory global description of soft hadronic observables. Some
discrepancies may be attributed to the absence of the final-state elastic
interactions among hadrons. Extrapolating Ti to higher values allows for global
predictions for soft hadronic physics at the LHC. We test Ti=400, 450, and 500
MeV, and observe the expected growth of particle multiplicities and the
increase of the flow, resulting in smaller slopes of the pT-spectra. The
elliptic flow of pions exhibits saturation, with v2 remaining practically
constant, while the HBT radii increase moderately with Ti.
