Error estimates for a Neumann problem in highly oscillating thin domains

Marcone C. Pereira; Ricardo P. Silva

doi:10.3934/dcds.2013.33.803

Article Contents

2013, Volume 33, Issue 2: 803-817. Doi: 10.3934/dcds.2013.33.803

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Error estimates for a Neumann problem in highly oscillating thin domains

Marcone C. Pereira^1, and
Ricardo P. Silva^2,

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

Received: April 30, 2011

Revised: June 30, 2012

Published: January 2013

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B25, 35B27, 74Q05.

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