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We give a prescription to perform the continuum limit of the $d$-dimensionalHubbard model in the presence of a harmonic trap at zero temperature. Weperform the continuum limit at fixed number of particles. In $d\geq3$ thelattice system of spin-1/2 particles is mapped into a non-interactingtwo-component Fermi gas in a harmonic trap. In $d=1$ and $d=2$ the particleswith opposite spin interact via a Dirac delta interaction. We show that theproperties of this continuum limit can be put in correspondence with thosederived applying the Trap-Size scaling (TSS) formalism to the confined Hubbardmodel in the so called Dilute Regime (fixed number of particles and weakconfinement). The correspondence in $d=1$ and $d=2$ has been tested comparingthe numerical results obtained for lattice system with those of the continuumlimit in the case of two-particle and in absence of spin-polarization($N=2$,$N_{\uparrow}=N_{\downarrow}=1$).

Trap effects and continuum limit of the Hubbard model in the presence of a harmonic potential