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Adaptivity and a Posteriori Error Control for Bifurcation Problems III: Incompressible Fluid Flow in Open Systems with O(2) Symmetry

Cliffe, Andrew; Hall, Edward; Houston, Paul; Phipps, Eric; Salinger, Andrew

Authors

Andrew Cliffe

PAUL HOUSTON paul.houston@nottingham.ac.uk
Professor of Computational and Applied Maths

Eric Phipps

Andrew Salinger



Abstract

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the critical Reynolds number at which a steady pitchfork bifurcation occurs when the underlying physical system possesses rotational and reflectional or O(2) symmetry. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual Weighted Residual approach, originally developed for the estimation of target functionals of the solution, to bifurcation problems. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented. Here, particular attention is devoted to the problem of flow through a cylindrical pipe with a sudden expansion, which represents a notoriously difficult computational problem.

Citation

Hall, E. J. C., Cliffe, K. A., Cliffe, A., Hall, E., Houston, P., Phipps, E. T., & Salinger, A. G. (2012). Adaptivity and a Posteriori Error Control for Bifurcation Problems III: Incompressible Fluid Flow in Open Systems with O(2) Symmetry. Journal of Scientific Computing, 52(1), 153-179. https://doi.org/10.1007/s10915-011-9545-8

Journal Article Type Article
Acceptance Date Sep 16, 2011
Online Publication Date Oct 14, 2011
Publication Date 2012-07
Deposit Date Feb 14, 2011
Publicly Available Date Oct 14, 2011
Journal Journal of Scientific Computing
Print ISSN 0885-7474
Electronic ISSN 1573-7691
Publisher Springer Verlag
Peer Reviewed Not Peer Reviewed
Volume 52
Issue 1
Pages 153-179
DOI https://doi.org/10.1007/s10915-011-9545-8
Keywords Theoretical Computer Science; General Engineering; Computational Theory and Mathematics; Software
Public URL http://eprints.nottingham.ac.uk/id/eprint/1437
Publisher URL http://link.springer.com/content/pdf/10.1007%2Fs10915-011-9545-8.pdf
Additional Information The final publication is available at link.springer.com

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