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

Burman, Erik and Fernández, Miguel A (2007) Continuous interior penalty finite element method for the time-dependent Navier-Stokes equations: space discretization and convergence. Numerische Mathematik, 107 (1). pp. 39-77. ISSN 0029-599X

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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 $L^2$-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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Erik Burman
Date Deposited: 06 Feb 2012 20:10
Last Modified: 14 May 2012 13:51
URI: http://sro.sussex.ac.uk/id/eprint/24483
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