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

journal contribution
posted on 2023-06-08, 05:17 authored by Erik Burman, Miguel A Fernández
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.

History

Publication status

  • Published

Journal

Numerische Mathematik

ISSN

0029-599X

Publisher

Springer Verlag

Issue

1

Volume

107

Page range

39-77

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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