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

Authors
  • Burman, Erik1
  • Fernández, Miguel A.2
  • 1 Institut d’analyse et de calcul scientifique, Ecole Polytechnique Fédérale de Lausanne, Station 8, Lausanne, CH-1015, Switzerland , Lausanne (Switzerland)
  • 2 INRIA, REO team, Rocquencourt BP 105, Le Chesnay Cedex, 78153, France , Le Chesnay Cedex (France)
Type
Published Article
Journal
Numerische Mathematik
Publisher
Springer-Verlag
Publication Date
May 16, 2007
Volume
107
Issue
1
Pages
39–77
Identifiers
DOI: 10.1007/s00211-007-0070-5
Source
Springer Nature
Keywords
License
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Abstract

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 L2-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.

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