, Volume 41, Issue 2, pp 89–113 | Cite as

The inf-sup condition for low order elements on anisotropic meshes

  • T. Apel
  • S. Nicaise


On a large class of two-dimensional anisotropic meshes, the inf-sup condition (stability) is proved for the triangular and quadrilateral finite element pairs suggested by Bernardi/Raugel and Fortin. As a consequence the pairs \({\cal P}_2-{\cal P}_0\), \({\cal Q}_2-{\cal P}_0\), and \({\cal Q}_2^\prime-{\cal P}_0\) turn out to be stable independent of the aspect ratio of the elements.


Aspect Ratio Large Class Order Element Element Pair Anisotropic Mesh 
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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  • T. Apel
    • 1
  • S. Nicaise
    • 2
  1. 1.Institut für Mathematik und Bauinformatik, Universität der Bundeswehr München, NeubibergGermany
  2. 2.Université de Valenciennes et du Hainaut Cambrésis, Institut des Sciences et Techniques de Valenciennes, ValenciennesFrance

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