4.5 Article

ERROR ESTIMATES FOR A NEUMANN PROBLEM IN HIGHLY OSCILLATING THIN DOMAINS

Journal

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
Volume 33, Issue 2, Pages 803-817

Publisher

AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2013.33.803

Keywords

Thin domains; correctors; homogenization; error estimate

Funding

  1. CNPq [305210/2008-4, 302847/2011-1]
  2. CAPES DGU [267/2008]
  3. FAPESP, Brazil [2008/53094-4, 2010/18790-0]
  4. FAPESP [2008/53094-4, 2012/06753-8]
  5. PROPe/UNESP, Brazil
  6. 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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