Partial Differential Equations with Oscillatory Coefficients

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


We present here some efficient techniques to approximate solutions of partial differential equations with oscillatory coefficients. We consider a simple one-dimensional case that still keeps most of the difficulties present in more sophisticated problems. We discuss three different approximation techniques: classical finite elements, homogenization, and Multiscale Finite Element methods (MsFEM). We show the advantages and pitfalls of each of the techniques, and present numerical results.


Finite Element Method Asymptotic Expansion Element Method Discretization Finite Element Approximation Multiscale Method 
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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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