Document Zbl 1175.76092

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Methods Appl. Mech. Eng.</a> <a href="/?q=in%3A208471" title="Articles in this Issue">196, No. 29-30, 2852-2862 (2007)</a>. </div> <div class="abstract">Summary: This paper proposes and analyzes a multi-level stabilized finite element method for the two-dimensional stationary Navier-Stokes equations approximated by the lowest equal-order finite element pairs. The method combines the new stabilized finite element method with the multi-level discretization under the assumption of the uniqueness condition. The multi-level stabilized finite element method consists of solving the nonlinear problem on the coarsest mesh and then performs one Newton correction step on each subsequent mesh thus only solving one large linear systems. The error analysis shows that the multi-level stabilized finite element method provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution solving the stationary Navier-Stokes equations on a fine mesh for an appropriate choice of mesh widths: $h_{j} \sim h^{2}_{j-1}, j = 1, \cdots , J$. Moreover, the numerical illustrations agree completely with the theoretical expectations. Therefore, the multi-level stabilized finite element method is more efficient than the standard one-level stabilized finite element method.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5194269">Cited in <strong>31</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A76M10" title="MSC2020">76M10</a> </td> <td class="space"> Finite element methods applied to problems in fluid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76D05" title="MSC2020">76D05</a> </td> <td class="space"> Navier-Stokes equations for incompressible viscous fluids </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35Q30" title="MSC2020">35Q30</a> </td> <td class="space"> Navier-Stokes equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65N30" title="MSC2020">65N30</a> </td> <td class="space"> Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3ANavier-Stokes+equations">Navier-Stokes equations</a>; <a href="/?q=ut%3Astabilized+finite+element+method">stabilized finite element method</a>; <a href="/?q=ut%3Ainf-sup+condition">inf-sup condition</a>; <a href="/?q=ut%3Amulti-level+discretization">multi-level discretization</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1175.76092" data-ciurl="/ci/05194269" data-biburl="/bibtex/05194269.bib" data-amsurl="/amsrefs/05194269.bib" data-xmlurl="/xml/05194269.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05194269.pdf" title="Zbl 1175.76092 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.cma.2006.12.007" aria-label="DOI for “A multi-level stabilized finite element method for the stationary Navier-Stokes equations”" title="10.1016/j.cma.2006.12.007">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Brezzi, F.; Douglas, J., Stabilized mixed methods for the Stokes problem, Numer. 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