  In this paper, we study the thin-film limit of the micromagnetic energy
functional in the presence of bulk Dzyaloshinskii-Moriya interaction (DMI). Our
analysis includes both a stationary $\Gamma$-convergence result for the
micromagnetic energy, as well as the identification of the asymptotic behavior
of the associated Landau-Lifshitz-Gilbert equation. In particular, we prove
that, in the limiting model, part of the DMI term behaves like the projection
of the magnetic moment onto the normal to the film, contributing this way to an
increase in the shape anisotropy arising from the magnetostatic self-energy.
Finally, we discuss a convergent finite element approach for the approximation
of the time-dependent case and use it to numerically compare the original
three-dimensional model with the two-dimensional thin-film limit.
