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

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Abstract

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

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Authors and Affiliations

  1. Institut für Mathematik und Bauinformatik, Universität der Bundeswehr München, Neubiberg, Germany

    T. Apel

  2. Institut des Sciences et Techniques de Valenciennes, Université de Valenciennes et du Hainaut Cambrésis, Valenciennes, France

    S. Nicaise

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  1. T. Apel
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  2. S. Nicaise
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Both the visit of the first author in Valenciennes and the visit of the second author in Chemnitz were financed by the DFG (German Research Foundation), Sonderforschungsbereich 393.

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Apel, T., Nicaise, S. The inf-sup condition for low order elements on anisotropic meshes. Calcolo 41, 89–113 (2004). https://doi.org/10.1007/BF02637257

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  • DOI: https://doi.org/10.1007/BF02637257

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