Stabilized finite element schemes for incompressible flow using Scott-Vogelius element

Burman, E and Linke, A (2008) Stabilized finite element schemes for incompressible flow using Scott-Vogelius element. Applied Numerical Mathematics, 58 (11). pp. 1704-1719. ISSN 0168-9274

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Abstract

We propose a stabilized mixed finite element method based on the ScottVogelius element for the Oseen equation. Here, only convection has to be stabilized since by construction both the discrete pressure and the divergence of the discrete velocities are controlled in the norm L2. As stabilization we propose either the local projection stabilization or the interior penalty stabilization based on the penalization of the gradient jumps over element edges. We prove a discrete infsup condition leading to optimal a priori error estimates. Moreover, convergence of the velocities is completely independent of the pressure regularity, and in the purely incompressible case the discrete velocities are pointwise divergence free. The theoretical considerations are illustrated by some numerical examples.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Erik Burman
Date Deposited: 06 Feb 2012 20:36
Last Modified: 04 Apr 2012 14:09
URI: http://sro.sussex.ac.uk/id/eprint/26976
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