Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe 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: | Conference or Workshop Item |
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2013
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| Online Access: | https://eprints.nottingham.ac.uk/29680/ |
| _version_ | 1848793830368739328 |
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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 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. |
| first_indexed | 2025-11-14T19:06:32Z |
| format | Conference or Workshop Item |
| id | nottingham-29680 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:06:32Z |
| publishDate | 2013 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-296802020-05-04T20:19:55Z https://eprints.nottingham.ac.uk/29680/ Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe 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 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. 2013 Conference or Workshop Item PeerReviewed Cliffe, Andrew, Hall, Edward and Houston, Paul (2013) Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows. In: Numerical Mathematics and Advanced Applications, ENUMATH 2011, 5-9 September 2011, Leicester, UK. http://link.springer.com/chapter/10.1007%2F978-3-642-33134-3_36 |
| spellingShingle | Cliffe, Andrew Hall, Edward Houston, Paul Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows |
| title | Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows |
| title_full | Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows |
| title_fullStr | Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows |
| title_full_unstemmed | Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows |
| title_short | Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows |
| title_sort | application of hp-adaptive discontinuous galerkin methods to bifurcation phenomena in pipe flows |
| url | https://eprints.nottingham.ac.uk/29680/ https://eprints.nottingham.ac.uk/29680/ |