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Mixed hp-FEM on anisotropic meshes II: Hanging nodes and tensor products of boundary layer meshes

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Summary.

The divergence stability of mixed hp Finite Element Methods for incompressible fluid flow is analyzed. A discrete inf-sup condition is proved for a general class of meshes. The meshes may be refined anisotropically, geometrically and may contain hanging nodes on geometric patches. The inf-sup constant is shown to be independent of the aspect ratio of the anisotropic elements and the dependence on the polynomial degree is analyzed. Numerical estimates of inf-sup constants confirm the theoretical results.

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Authors and Affiliations

  1. Seminar für Angewandte Mathematik, ETH Zürich, Rämistrasse 101, CH-8092 Zürich, Switzerland , , , , , , CH

    Dominik Schötzau & Christoph Schwab

  2. Institut für Mathematik und Geometrie, Universität Innsbruck, Technikerstrasse 13, A-6020 Innsbruck, Austria , , , , , , AT

    Rolf Stenberg

Authors
  1. Dominik Schötzau
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  2. Christoph Schwab
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  3. Rolf Stenberg
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Received October 13, 1997 / Revised version received June 8, 1998 / Published online July 28, 1999

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Schötzau, D., Schwab, C. & Stenberg, R. Mixed hp-FEM on anisotropic meshes II: Hanging nodes and tensor products of boundary layer meshes. Numer. Math. 83, 667–697 (1999). https://doi.org/10.1007/s002119900074

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  • DOI: https://doi.org/10.1007/s002119900074

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