Adaptivity and a Posteriori Error Control for Bifurcation Problems II: Incompressible Fluid Flow in Open Systems with Z2 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...
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| Veröffentlicht in: | Journal of scientific computing 2011-06, Vol.47 (3), p.389-418 |
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| container_title | Journal of scientific computing |
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| creator | Cliffe, K. Andrew Hall, Edward J. C. Houston, Paul Phipps, Eric T. Salinger, Andrew G. |
| 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. |
| doi_str_mv | 10.1007/s10915-010-9453-3 |
| format | Article |
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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.</description><identifier>ISSN: 0885-7474</identifier><identifier>EISSN: 1573-7691</identifier><identifier>DOI: 10.1007/s10915-010-9453-3</identifier><language>eng</language><publisher>Boston: Springer US</publisher><subject>Algorithms ; Bifurcations ; Computation ; Computational fluid dynamics ; Computational Mathematics and Numerical Analysis ; Error analysis ; Errors ; Fluid flow ; Grid refinement (mathematics) ; Hopf bifurcation ; Incompressible flow ; Incompressible fluids ; Mathematical analysis ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Open systems ; Reynolds number ; Symmetry ; Theoretical</subject><ispartof>Journal of scientific computing, 2011-06, Vol.47 (3), p.389-418</ispartof><rights>Springer Science+Business Media, LLC 2011</rights><rights>Springer Science+Business Media, LLC 2011.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10915-010-9453-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2918312561?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,776,780,21367,27901,27902,33721,33722,41464,42533,43781,51294</link.rule.ids></links><search><creatorcontrib>Cliffe, K. Andrew</creatorcontrib><creatorcontrib>Hall, Edward J. C.</creatorcontrib><creatorcontrib>Houston, Paul</creatorcontrib><creatorcontrib>Phipps, Eric T.</creatorcontrib><creatorcontrib>Salinger, Andrew G.</creatorcontrib><title>Adaptivity and a Posteriori Error Control for Bifurcation Problems II: Incompressible Fluid Flow in Open Systems with Z2 Symmetry</title><title>Journal of scientific computing</title><addtitle>J Sci Comput</addtitle><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.</description><subject>Algorithms</subject><subject>Bifurcations</subject><subject>Computation</subject><subject>Computational fluid dynamics</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Error analysis</subject><subject>Errors</subject><subject>Fluid flow</subject><subject>Grid refinement (mathematics)</subject><subject>Hopf bifurcation</subject><subject>Incompressible flow</subject><subject>Incompressible fluids</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Open systems</subject><subject>Reynolds number</subject><subject>Symmetry</subject><subject>Theoretical</subject><issn>0885-7474</issn><issn>1573-7691</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNpdkU9LwzAYh4MoOKcfwFvAi5dq3qRNWm9zbFoYOFAvXkrXpJrRJjVpHbv6SfwsfjIzJghe3n88_HjhQegcyBUQIq49kAySiACJsjhhETtAI0gEiwTP4BCNSJomkYhFfIxOvF8TQrI0oyP0OZFl1-sP3W9xaSQu8dL6XjltncYz56zDU2t6Zxtch_lW14Oryl5bg5fOrhrV-u-vPL_Buals2znlvQ5XPG8GLUO1G6wNfuiUwY_bENx6vNH9G36hYW9b1bvtKTqqy8ars98-Rs_z2dP0Plo83OXTySLqgMQsilPGqaqUZFVF6ipOFHDgJaWVJIyCpEoqwbmCmAtJMpFkkCbAVjFnQma1ZGN0uc_tnH0flO-LVvtKNU1plB18AVwAEwIIC-jFP3RtB2fCdwUNsQxowiFQdE_5zmnzqtwfBaTYaSn2WoqgpdhpKRj7AacYgPI</recordid><startdate>20110601</startdate><enddate>20110601</enddate><creator>Cliffe, K. 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C. ; Houston, Paul ; Phipps, Eric T. ; Salinger, Andrew G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p1043-48362eced3cc0fc45e1616a22cd0321d2ede766e1467d0975918513b4637d9fd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Algorithms</topic><topic>Bifurcations</topic><topic>Computation</topic><topic>Computational fluid dynamics</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Error analysis</topic><topic>Errors</topic><topic>Fluid flow</topic><topic>Grid refinement (mathematics)</topic><topic>Hopf bifurcation</topic><topic>Incompressible flow</topic><topic>Incompressible fluids</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Open systems</topic><topic>Reynolds number</topic><topic>Symmetry</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cliffe, K. Andrew</creatorcontrib><creatorcontrib>Hall, Edward J. 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Andrew</au><au>Hall, Edward J. C.</au><au>Houston, Paul</au><au>Phipps, Eric T.</au><au>Salinger, Andrew G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Adaptivity and a Posteriori Error Control for Bifurcation Problems II: Incompressible Fluid Flow in Open Systems with Z2 Symmetry</atitle><jtitle>Journal of scientific computing</jtitle><stitle>J Sci Comput</stitle><date>2011-06-01</date><risdate>2011</risdate><volume>47</volume><issue>3</issue><spage>389</spage><epage>418</epage><pages>389-418</pages><issn>0885-7474</issn><eissn>1573-7691</eissn><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.</abstract><cop>Boston</cop><pub>Springer US</pub><doi>10.1007/s10915-010-9453-3</doi><tpages>30</tpages></addata></record> |
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| subjects | Algorithms Bifurcations Computation Computational fluid dynamics Computational Mathematics and Numerical Analysis Error analysis Errors Fluid flow Grid refinement (mathematics) Hopf bifurcation Incompressible flow Incompressible fluids Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Open systems Reynolds number Symmetry Theoretical |
| title | Adaptivity and a Posteriori Error Control for Bifurcation Problems II: Incompressible Fluid Flow in Open Systems with Z2 Symmetry |
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