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Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry

Cliffe, Andrew; Hall, Edward; Houston, Paul; Phipps, Eric T.; Salinger, Andrew G.

Authors

Andrew Cliffe Andrew.Cliffe@nottingham.ac.uk

Edward Hall Edward.Hall@nottingham.ac.uk

Paul Houston Paul.Houston@nottingham.ac.uk

Eric T. Phipps etphipp@sandia.gov

Andrew G. Salinger agsalin@sandia.gov



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 or Hopf bifurcation occurs when the underlying physical system possesses reflectional or Z_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.

Journal Article Type Article
Journal Journal of Scientific Computing
Print ISSN 0885-7474
Electronic ISSN 0885-7474
Publisher Humana Press
Peer Reviewed Not Peer Reviewed
APA6 Citation Cliffe, A., Hall, E., Houston, P., Phipps, E. T., & Salinger, A. G. Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry. Manuscript submitted for publication
Publisher URL http://www.springer.com/mathematics/numerical+and+computational+mathematics/journal/10915
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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