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Application of hp–Adaptive Discontinuous Galerkin Methods to Bifurcation Phenomena in Pipe Flows

In: Numerical Mathematics and Advanced Applications 2011

Author

Listed:
  • K. A. Cliffe

    (University of Nottingham, University Park, School of Mathematical Sciences)

  • E. J. C. Hall

    (University of Nottingham, University Park, School of Mathematical Sciences)

  • P. Houston

    (University of Nottingham, University Park, School of Mathematical Sciences)

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.

Suggested Citation

  • K. A. Cliffe & E. J. C. Hall & P. Houston, 2013. "Application of hp–Adaptive Discontinuous Galerkin Methods to Bifurcation Phenomena in Pipe Flows," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 333-340, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_36
    DOI: 10.1007/978-3-642-33134-3_36
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