Edge stabilization for the generalized Stokes problem: a continuous interior penalty method

Burman, Erik and Hansbo, Peter (2006) Edge stabilization for the generalized Stokes problem: a continuous interior penalty method. Computer Methods in Applied Mechanics and Engineering, 195 (19-22). pp. 2393-2410. ISSN 0045-7825

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Abstract

In this note we introduce and analyze a stabilized finite element method for the generalized Stokes equation. Stability is obtained by adding a least squares penalization of the gradient jumps across element boundaries. The method can be seen as a higher order version of the BrezziPitkranta penalty stabilization [F. Brezzi, J. Pitkranta, On the stabilization of finite element approximations of the Stokes equations, in: W. Hackbusch (Ed.), Efficient Solution of Elliptic Systems, Vieweg, 1984], but gives better resolution on the boundary for the Stokes equation than does classical Galerkin least-squares formulation. We prove optimal and quasi-optimal convergence properties for Stokes problem and for the porous media models of Darcy and Brinkman. Some numerical examples are given.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Erik Burman
Date Deposited: 06 Feb 2012 19:13
Last Modified: 04 Apr 2012 08:04
URI: http://sro.sussex.ac.uk/id/eprint/19618
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