Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry
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 estimat...
| Main Authors: | , , , , |
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| Format: | Article |
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Springer Netherlands
2010
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| Online Access: | https://eprints.nottingham.ac.uk/1257/ |
| _version_ | 1848790571013898240 |
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| author | Cliffe, Andrew Hall, Edward Houston, Paul Phipps, Eric T. Salinger, Andrew G. |
| author_facet | Cliffe, Andrew Hall, Edward Houston, Paul Phipps, Eric T. Salinger, Andrew G. |
| author_sort | Cliffe, Andrew |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T18:14:43Z |
| format | Article |
| id | nottingham-1257 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:14:43Z |
| publishDate | 2010 |
| publisher | Springer Netherlands |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-12572020-05-04T20:25:07Z https://eprints.nottingham.ac.uk/1257/ 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. 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. Springer Netherlands 2010-03 Article NonPeerReviewed Cliffe, Andrew, Hall, Edward, Houston, Paul, 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) http://www.springer.com/mathematics/numerical+and+computational+mathematics/journal/10915 |
| spellingShingle | Cliffe, Andrew Hall, Edward Houston, Paul Phipps, Eric T. Salinger, Andrew G. Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry |
| title | Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry |
| title_full | Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry |
| title_fullStr | Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry |
| title_full_unstemmed | Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry |
| title_short | Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry |
| title_sort | adaptivity and a posteriori error control for bifurcation problems ii: incompressible fluid flow in open systems with z_2 symmetry |
| url | https://eprints.nottingham.ac.uk/1257/ https://eprints.nottingham.ac.uk/1257/ |