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

Cliffe, Andrew and Hall, Edward and Houston, Paul and Phipps, Eric T. and Salinger, Andrew G. (2010) Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry. Journal of Scientific Computing . ISSN 0885-7474 (Submitted)

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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.

Item Type: Article
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Depositing User: Houston, Paul
Date Deposited: 25 Mar 2010 09:49
Last Modified: 23 Jun 2011 06:51
URI: http://eprints.nottingham.ac.uk/id/eprint/1257

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