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Homogenization Problem in a Domain with Double Oscillating Boundary

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  • Jie Zhao
  • Juan Wang

Abstract

In this paper, we study the convergence of solutions for homogenization problems about the Poisson equation in a domain with double oscillating locally periodic boundary. Such a problem arises in the processing of devices with very small features. We utilize second-order Taylor expansion of boundary data in combination with boundary correctors to obtain the convergence rate in -norm. This work explores the domain with double oscillating boundary and also shows the influence of the amplitudes and periods of the oscillations to convergence rates of solutions.

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  • Jie Zhao & Juan Wang, 2018. "Homogenization Problem in a Domain with Double Oscillating Boundary," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-14, October.
    • Handle: RePEc:hin:jnlmpe:3746562
    DOI: 10.1155/2018/3746562
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