The formation and evolution of the elliptic flow pattern in $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s}=5.5A$ TeV and in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s}=200A$ GeV are analyzed for different hadron species within the framework of the HYDJET$++$ Monte Carlo model. The model contains both hydrodynamic state and jets, thus allowing for a study of the interplay between the soft and hard processes. It is found that jets terminate the rise of the elliptic flow with increasing transverse momentum. Since jets are more influential at the Large Hadron Collider (LHC) than at the Relativistic Heavy Ion Collider (RHIC), the elliptic flow at LHC should be weaker than that at RHIC. The influence of resonance decays on particle elliptic flow is also investigated. These final state interactions enhance the low-${p}_{T}$ part of the ${v}_{2}$ of pions and light baryons and work toward the fulfillment of idealized constituent quark scaling.