# American Institute of Mathematical Sciences

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February  2013, 33(2): 803-817. doi: 10.3934/dcds.2013.33.803

## Error estimates for a Neumann problem in highly oscillating thin domains

 1 Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, São Paulo, SP, Brazil 2 Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista, Rio Claro, SP, Brazil

Received  May 2011 Revised  July 2012 Published  September 2012

In this work we analyze the convergence of solutions of the Poisson equation with Neumann boundary conditions in a two-dimensional thin domain with highly oscillatory behavior. We consider the case where the height of the domain, amplitude and period of the oscillations are all of the same order, and given by a small parameter $\epsilon>0$. Using an appropriate corrector approach, we show strong convergence and give error estimates when we replace the original solutions by the first-order expansion through the Multiple-Scale Method.
Citation: Marcone C. Pereira, Ricardo P. Silva. Error estimates for a Neumann problem in highly oscillating thin domains. Discrete & Continuous Dynamical Systems, 2013, 33 (2) : 803-817. doi: 10.3934/dcds.2013.33.803
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