  In this paper we are concerned with convergence of solutions of the Poisson
equation with Neumann boundary conditions in a two-dimensional thin domain
exhibiting highly oscillatory behavior in part of its boundary. We deal with
the resonant case in which the height, amplitude and period of the oscillations
are all of the same order which is given by a small parameter $\epsilon > 0$.
Applying an appropriate corrector approach we get strong convergence when we
replace the original solutions by a kind of first-order expansion through the
Multiple-Scale Method.
