Modeling PDEs in Domains with Rough Boundaries

  • Alexandre L. Madureira
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)


We discuss here PDEs defined in domains where at least part of the boundary is rugous. The fully discretization of such domains can be very expensive, and we show two ways to decrease such burden. When the wrinkles are periodic, one way is to avoid the expensive discretization of the rough domain altogether, replacing the rough domain by a smooth one and changing the boundary conditions in such a way that the geometry of the wrinkles is captured. For a general domain, a possibility is to use a domain decomposition approach, solving local problems in parallel in the spirit of the Multiscale Finite Element Method. Asymptotic expansions play a key role in both alternatives, motivating the development of models, and helping in deriving error estimates.


Finite Element Method Asymptotic Expansion Multiscale Method Cell Problem Rough Boundary 
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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Alexandre L. Madureira
    • 1
    • 2
  1. 1.Laboratório Nacional de Computação Científica-LNCCPetrópolisBrazil
  2. 2.Fundação Getúlio Vargas-FGVRio de JaneiroBrazil

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