  In this paper, we consider homogenization of the Landau-Lifshitz equation
with a highly oscillatory material coefficient with period $\varepsilon$
modeling a ferromagnetic composite. We derive equations for the homogenized
solution to the problem and the corresponding correctors and obtain estimates
for the difference between the exact and homogenized solution as well as
corrected approximations to the solution. Convergence rates in $\varepsilon$
over times $O(\varepsilon^\sigma)$ with $0\leq \sigma\leq 2$ are given in the
Sobolev norm $H^q$, where $q$ is limited by the regularity of the solution to
the detailed Landau-Lifshitz equation and the homogenized equation. The rates
depend on $q$, $\sigma$ and the the number of correctors.
