Based on the analytic model of Feshbach resonances in harmonic traps described in Phys. Rev. A 83, 030701 (2011) a Bose-Hubbard model is introduced that provides an accurate description of two atoms in an optical lattice at a Feshbach resonance with only a small number of Bloch bands. The approach circumvents the problem that the eigenenergies in the presence of a delta-like coupling do not converge to the correct energies, if an uncorrelated basis is used. The predictions of the Bose-Hubbard model are compared to non-perturbative calculations for both the stationary states and the time-dependent wavefunction during an acceleration of the lattice potential. For this purpose, a square-well interaction potential is introduced, which allows for a realistic description of Feshbach resonances within non-perturbative single-channel calculations.
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