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

Cliffe, Andrew; Hall, Edward; Houston, Paul; Phipps, Eric T.; Salinger, Andrew G.

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.

Citation

Cliffe, A., Hall, E., Houston, P., Phipps, E. T., & Salinger, A. G. Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry. Manuscript submitted for publication

• Journal Article Type: Article
• Deposit Date: Mar 25, 2010
• Peer Reviewed: Not Peer Reviewed
• Public URL: https://nottingham-repository.worktribe.com/output/1012104