, Volume 41, Issue 2, pp 89-113

First online:

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

  • T. ApelAffiliated withInstitut für Mathematik und Bauinformatik, Universität der Bundeswehr München, Neubiberg
  • , S. NicaiseAffiliated withUniversité de Valenciennes et du Hainaut Cambrésis, Institut des Sciences et Techniques de Valenciennes, Valenciennes

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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.