Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows

Cliffe, Andrew and Hall, Edward and Houston, Paul (2013) Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows. In: Numerical Mathematics and Advanced Applications, ENUMATH 2011, 5-9 September 2011, Leicester, UK.

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Abstract

In this article we consider the a posteriori error estimation and adaptive mesh refinement of hp-version 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 hp-adaptively refined computational meshes are presented.

Item Type: Conference or Workshop Item (Paper)
Additional Information: Cliffe, A., Hall, E., Houston, P., Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows, in: Numerical Mathematics and Advanced Applications 2011: proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011, editors, A. Cangiani ... [et al.]. Berlin : Springer, 2013. ISBN: 9783642331336, pp. 333-340. doi: 10.1007/978-3-642-33134-3_36
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Depositing User: Houston, Paul
Date Deposited: 28 Aug 2015 13:46
Last Modified: 14 Sep 2016 06:48
URI: http://eprints.nottingham.ac.uk/id/eprint/29680

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