Adaptivity and a posteriori error control for bifurcation problems III: incompressible fluid flow in open systems with O(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
2012
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| Online Access: | https://eprints.nottingham.ac.uk/1437/ |
| _version_ | 1848790605156581376 |
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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 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 adaptively refined computational meshes are presented. Here, particular attention is devoted to the problem of flow through a cylindrical pipe with a sudden expansion, which represents a notoriously difficult computational problem. |
| first_indexed | 2025-11-14T18:15:16Z |
| format | Article |
| id | nottingham-1437 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:15:16Z |
| publishDate | 2012 |
| publisher | Springer Netherlands |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-14372020-05-04T20:22:20Z https://eprints.nottingham.ac.uk/1437/ Adaptivity and a posteriori error control for bifurcation problems III: incompressible fluid flow in open systems with O(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 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 adaptively refined computational meshes are presented. Here, particular attention is devoted to the problem of flow through a cylindrical pipe with a sudden expansion, which represents a notoriously difficult computational problem. Springer Netherlands 2012 Article NonPeerReviewed Cliffe, Andrew, Hall, Edward, Houston, Paul, Phipps, Eric T. and Salinger, Andrew G. (2012) Adaptivity and a posteriori error control for bifurcation problems III: incompressible fluid flow in open systems with O(2) symmetry. Journal of Scientific Computing, 52 (2). pp. 153-179. ISSN 0885-7474 (Submitted) http://link.springer.com/content/pdf/10.1007%2Fs10915-011-9545-8.pdf doi:10.1007/s10915-011-9545-8 doi:10.1007/s10915-011-9545-8 |
| spellingShingle | Cliffe, Andrew Hall, Edward Houston, Paul Phipps, Eric T. Salinger, Andrew G. Adaptivity and a posteriori error control for bifurcation problems III: incompressible fluid flow in open systems with O(2) symmetry |
| title | Adaptivity and a posteriori error control for bifurcation problems III: incompressible fluid flow in open systems with O(2) symmetry |
| title_full | Adaptivity and a posteriori error control for bifurcation problems III: incompressible fluid flow in open systems with O(2) symmetry |
| title_fullStr | Adaptivity and a posteriori error control for bifurcation problems III: incompressible fluid flow in open systems with O(2) symmetry |
| title_full_unstemmed | Adaptivity and a posteriori error control for bifurcation problems III: incompressible fluid flow in open systems with O(2) symmetry |
| title_short | Adaptivity and a posteriori error control for bifurcation problems III: incompressible fluid flow in open systems with O(2) symmetry |
| title_sort | adaptivity and a posteriori error control for bifurcation problems iii: incompressible fluid flow in open systems with o(2) symmetry |
| url | https://eprints.nottingham.ac.uk/1437/ https://eprints.nottingham.ac.uk/1437/ https://eprints.nottingham.ac.uk/1437/ |