Correctors for the Neumann problem in thin domains with locally periodic\n oscillatory structure

2013/11/13 by Marcone C. Pereira, Pereira, Marcone C., da Silva +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1311.3073

openalex publication_date 2013/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we are concerned with convergence of solutions of the Poisson\nequation with Neumann boundary conditions in a two-dimensional thin domain\nexhibiting highly oscillatory behavior in part of its boundary. We deal with\nthe resonant case in which the height, amplitude and period of the oscillations\nare all of the same order which is given by a small parameter \ε > 0.\nApplying an appropriate corrector approach we get strong convergence when we\nreplace the original solutions by a kind of first-order expansion through the\nMultiple-Scale Method.\n

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