# A finite element method with edge oriented stabilization for the time-dependent Navier-Stokes equations: space discretization and convergence

1 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
Abstract : This work focuses on the numerical analysis of a finite element method with edge oriented 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 edges. 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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https://hal.inria.fr/inria-00070378
Contributor : Rapport de Recherche Inria <>
Submitted on : Friday, May 19, 2006 - 8:18:59 PM
Last modification on : Tuesday, May 14, 2019 - 10:13:46 AM
Long-term archiving on: Sunday, April 4, 2010 - 9:04:37 PM

### Identifiers

• HAL Id : inria-00070378, version 1

### Citation

Erik Burman, Miguel Angel Fernández. A finite element method with edge oriented stabilization for the time-dependent Navier-Stokes equations: space discretization and convergence. [Research Report] RR-5630, INRIA. 2005, pp.42. ⟨inria-00070378⟩

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