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Continuous interior penalty finite element method for the time-dependent Navier-Stokes equations: space discretization and convergence

Burman, Erik ; Fernández, Miguel

In: Numerische Mathematik, 2007, vol. 107, no. 1, p. 39-77

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    Titel
    • Continuous interior penalty finite element method for the time-dependent Navier-Stokes equations: space discretization and convergence
    Autor
    • Burman, Erik. Ecole Polytechnique Fédérale de Lausanne, Institut d'analyse et de calcul scientifique, Station 8, CH-1015, Lausanne, Switzerland
    • Fernández, Miguel. INRIA, REO team, Rocquencourt BP 105, 78153, Le Chesnay Cedex, France
    Dokumententyp
    • Postprint
    Sprache
    • Englisch
    Veröffentlicht in
    • Numerische Mathematik, 2007, vol. 107, no. 1, p. 39-77. Springer-Verlag
    Andere elektronische Ausgabe
    Klassifikation
    • Informatik
    OAI-PMH-ID
    • oai:doc.rero.ch:317859
    Summary
    This paper focuses on the numerical analysis of a finite element method with stabilization for the unsteady incompressible Navier-Stokes equations. Incompressibility and convective effects are both stabilized adding an interior penalty term giving L 2-control of the jump of the gradient of the approximate solution over the internal faces. Using continuous equal-order finite elements for both velocities and pressures, in a space semi-discretized formulation, we prove convergence of the approximate solution. The error estimates hold irrespective of the Reynolds number, and hence also for the incompressible Euler equations, provided the exact solution is smooth