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Adaptivity and a Posteriori Error Control for Bifurcation Problems II: Incompressible Fluid Flow in Open Systems with Z 2 Symmetry

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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.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

    K. Andrew Cliffe, Edward J. C. Hall & Paul Houston

  2. Computer Science Research Institute, Sandia National Laboratories, Albuquerque, NM, USA

    Eric T. Phipps & Andrew G. Salinger

Authors
  1. K. Andrew Cliffe
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  2. Edward J. C. Hall
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  3. Paul Houston
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  4. Eric T. Phipps
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  5. Andrew G. Salinger
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Correspondence to Paul Houston.

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Cliffe, K.A., Hall, E.J.C., Houston, P. et al. Adaptivity and a Posteriori Error Control for Bifurcation Problems II: Incompressible Fluid Flow in Open Systems with Z 2 Symmetry. J Sci Comput 47, 389–418 (2011). https://doi.org/10.1007/s10915-010-9453-3

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  • DOI: https://doi.org/10.1007/s10915-010-9453-3

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