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

Cliffe, Andrew; Hall, Edward; Houston, Paul

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.

Citation

Cliffe, A., Hall, E., & Houston, P. (2013). Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows.

• Conference Name: Numerical Mathematics and Advanced Applications, ENUMATH 2011
• End Date: Sep 9, 2011
• Publication Date: Jan 1, 2013
• Deposit Date: Aug 28, 2015
• Peer Reviewed: Peer Reviewed
• Public URL: https://nottingham-repository.worktribe.com/output/1003691
• Publisher URL: http://link.springer.com/chapter/10.1007%2F978-3-642-33134-3_36
• 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
• Contract Date: Aug 24, 2017