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


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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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).

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  • Isotropic Element
  • Mixed Finite Element Method
  • Anisotropic Mesh
  • Hanging Node
  • Regular Node