  In this work we analyze convergence of solutions for the Laplace operator
with Neumann boundary conditions in a two-dimensional highly oscillating domain
which degenerates into a segment (thin domains) of the real line. We consider
the case where the height of the thin domain, amplitude and period of the
oscillations are all of the same order, given by a small parameter $\epsilon$.
We investigate strong convergence properties of the solutions using an
appropriate corrector approach. We also give error estimates when we replace
the original solutions for the second-order expansion through the
Multiple-Scale Method.
