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On the enforcement of the zero mean pressure condition in the spectral element approximation of the Stokes problem

Gwynllyw, D. Rhys; Phillips, T. N.

Authors

D. Rhys Gwynllyw

T. N. Phillips



Abstract

This paper considers the spectral element approximation of the Stokes problem and the conditioning of the resulting discrete problem. The well-posedness of the variational formulation of the Stokes problem and, in particular, the uniqueness of the pressure has been demonstrated when the subspace of square-integrable functions having vanishing mean is chosen for the pressure space. In the discrete setting a conforming subspace is chosen for the discrete pressure space and the analysis of the discrete problem is based on this choice. However, this space is not used in practical implementations of finite or spectral element methods for the Stokes problem. In this paper it is shown how the zero volume condition on the pressure may be accommodated within the trial space by modifying the continuity equation in a consistent manner. The dependence of the condition number of the Uzawa operator and the accuracy of the spectral element approximation on the weighting factor is investigated. © 2005 Elsevier B.V. All rights reserved.

Citation

Gwynllyw, D. R., & Phillips, T. N. (2006). On the enforcement of the zero mean pressure condition in the spectral element approximation of the Stokes problem. Computer Methods in Applied Mechanics and Engineering, 195(9-12), 1027-1049. https://doi.org/10.1016/j.cma.2005.04.004

Journal Article Type Article
Publication Date Feb 1, 2006
Journal Computer Methods in Applied Mechanics and Engineering
Print ISSN 0045-7825
Publisher Elsevier
Peer Reviewed Not Peer Reviewed
Volume 195
Issue 9-12
Pages 1027-1049
DOI https://doi.org/10.1016/j.cma.2005.04.004
Keywords enforcement, zero mean pressure condition, spectral element approximation, Stokes problem
Public URL https://uwe-repository.worktribe.com/output/1041685
Publisher URL http://dx.doi.org/10.1016/j.cma.2005.04.004


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