Error estimates for a Neumann problem in highly oscillating thin domains

Abstract

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.