Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
Volume 33, Issue 2, Pages 803-817Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2013.33.803
Keywords
Thin domains; correctors; homogenization; error estimate
Categories
Funding
- CNPq [305210/2008-4, 302847/2011-1]
- CAPES DGU [267/2008]
- FAPESP, Brazil [2008/53094-4, 2010/18790-0]
- FAPESP [2008/53094-4, 2012/06753-8]
- PROPe/UNESP, Brazil
- Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) [10/18790-0] Funding Source: FAPESP
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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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