ERROR ESTIMATES FOR A NEUMANN PROBLEM IN HIGHLY OSCILLATING THIN DOMAINS

Author(s)

Pereira, Marcone C. ^[1] ; Silva, Ricardo P. ^[2]

Affiliation

^[1] Univ Sao Paulo, Escola Artes Ciencias & Humanidades, Sao Paulo - Brazil

^[2] Univ Estadual Paulista, Inst Geociencias & Ciencias Exatas, Rio Claro, SP - Brazil

• Document type: Journal article
• Source: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 33, n. 2, p. 803-817, FEB 2013.
• Web of Science Citations: 14

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. (AU)

• FAPESP's process: 12/06753-8 - Continuity of global attractors: Correctors and convergence rates
• Grantee: Ricardo Parreira da Silva
• Support Opportunities: Regular Research Grants
• FAPESP's process: 10/18790-0 - Asymptotic behavior and geometric of partial differential equations
• Grantee: Marcone Corrêa Pereira
• Support Opportunities: Regular Research Grants