hp-Adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows
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 er...
| Main Authors: | , , |
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| Format: | Article |
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Elsevier
2014
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| Online Access: | https://eprints.nottingham.ac.uk/1611/ |
| _version_ | 1848790638436286464 |
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| author | Cliffe, Andrew Hall, Edward Houston, Paul |
| author_facet | Cliffe, Andrew Hall, Edward Houston, Paul |
| 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 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 either reflectional Z_2 symmetry, or rotational and reflectional 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 for both two- and three-dimensional problems. In the latter case, 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 | 2025-11-14T18:15:48Z |
| format | Article |
| id | nottingham-1611 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:15:48Z |
| publishDate | 2014 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-16112020-05-04T16:44:03Z https://eprints.nottingham.ac.uk/1611/ hp-Adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows Cliffe, Andrew Hall, Edward Houston, Paul 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 either reflectional Z_2 symmetry, or rotational and reflectional 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 for both two- and three-dimensional problems. In the latter case, particular attention is devoted to the problem of flow through a cylindrical pipe with a sudden expansion, which represents a notoriously difficult computational problem. Elsevier 2014-03-30 Article PeerReviewed Cliffe, Andrew, Hall, Edward and Houston, Paul (2014) hp-Adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows. Computers and Mathematics with Applications, 67 (4). pp. 796-806. ISSN 0898-1221 https://www.sciencedirect.com/science/article/pii/S0898122113005919 doi:10.1016/j.camwa.2013.09.024 doi:10.1016/j.camwa.2013.09.024 |
| spellingShingle | Cliffe, Andrew Hall, Edward Houston, Paul hp-Adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows |
| title | hp-Adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows |
| title_full | hp-Adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows |
| title_fullStr | hp-Adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows |
| title_full_unstemmed | hp-Adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows |
| title_short | hp-Adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows |
| title_sort | hp-adaptive discontinuous galerkin methods for bifurcation phenomena in open flows |
| url | https://eprints.nottingham.ac.uk/1611/ https://eprints.nottingham.ac.uk/1611/ https://eprints.nottingham.ac.uk/1611/ |