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MsFEM à la Crouzeix-Raviart for Highly Oscillatory Elliptic Problems

  • Claude Le Bris
  • Frédéric Legoll
  • Alexei Lozinski

Abstract

We introduce and analyze a multiscale finite element type method (MsFEM) in the vein of the classical Crouzeix-Raviart finite element method that is specifically adapted for highly oscillatory elliptic problems. We illustrate numerically the efficiency of the approach and compare it with several variants of MsFEM.

Keywords

Homogenization Finite elements Galerkin methods Highly oscillatory PDE 

Mathematics Subject Classification

35B27 65M60 65M12 

Notes

Acknowledgements

The third author acknowledges the hospitality of INRIA. We thank William Minvielle for his remarks on a preliminary version of this article.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Claude Le Bris
    • 1
    • 2
  • Frédéric Legoll
    • 1
    • 2
  • Alexei Lozinski
    • 3
    • 4
  1. 1.École Nationale des Ponts et ChausséesMarne-La-Vallée Cedex 2France
  2. 2.MICMAC project-teamINRIA RocquencourtLe Chesnay CedexFrance
  3. 3.Institut de Mathématiques de ToulouseUniversité Paul SabatierToulouse Cedex 9France
  4. 4.Laboratoire de Mathématiques CNRS UMR 6623Université de Franche-ComtéBesançon CedexFrance

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