Document Zbl 1529.65076

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Model. Numer. Anal.</a> <a href="/?q=in%3A496768" title="Articles in this Issue">57, No. 2, 467-490 (2023)</a>. </div> <div class="abstract">Summary: Proper EMA-balance (balance of kinetic energy, linear momentum and angular momentum), pressure-robustness and Re-semi-robustness (<span class="zbmathjax-textit">Re</span>: Reynolds number) are three important properties of Navier-Stokes simulations with exactly divergence-free elements. This EMA-balance makes a method conserve kinetic energy, linear momentum and angular momentum in an appropriate sense; pressure-robustness means that the velocity errors are independent of the pressure; <span class="zbmathjax-textit">Re</span>-semi-robustness means that the constants appearing in the error bounds of kinetic and dissipation energies do not explicitly depend on inverse powers of the viscosity. In this paper, based on the pressure-robust reconstruction framework and certain suggested reconstruction operators in [<span class="zbmathjax-textit">A. Linke</span> and <span class="zbmathjax-textit">C. Merdon</span>, Comput. Methods Appl. Mech. Eng. 311, 304–326 (2016; <a href="/1439.76083">Zbl 1439.76083</a>)], we propose a reconstruction method for a class of non-divergence-free simplicial elements which admits almost all the above properties. The only exception is the energy balance, where kinetic energy should be replaced by a suitably redefined discrete energy. The lowest order case is the Bernardi-Raugel element on general shape-regular meshes. Some numerical comparisons with exactly divergence-free methods, the original pressure-robust reconstruction methods and the EMAC method are provided to confirm our theoretical results.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7689056">Cited in <strong>3</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M60" title="MSC2020">65M60</a> </td> <td class="space"> Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M06" title="MSC2020">65M06</a> </td> <td class="space"> Finite difference methods for initial value and initial-boundary value problems involving PDEs </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><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M12" title="MSC2020">65M12</a> </td> <td class="space"> Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M15" title="MSC2020">65M15</a> </td> <td class="space"> Error bounds for initial value and initial-boundary value problems involving PDEs </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%3A76D17" title="MSC2020">76D17</a> </td> <td class="space"> Viscous vortex flows </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></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Afinite+element+methods">finite element methods</a>; <a href="/?q=ut%3Aunsteady+Navier-Stokes+equations">unsteady Navier-Stokes equations</a>; <a href="/?q=ut%3Apressure-robustness">pressure-robustness</a>; <a href="/?q=ut%3AEMAC+formulation">EMAC formulation</a>; <a href="/?q=ut%3Are-semi-robustness">re-semi-robustness</a></div><div class="keywords"> <h3>Citations:</h3><a href="/1439.76083">Zbl 1439.76083</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 1529.65076" data-ciurl="/ci/07689056" data-biburl="/bibtex/07689056.bib" data-amsurl="/amsrefs/07689056.bib" data-xmlurl="/xml/07689056.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07689056.pdf" title="Zbl 1529.65076 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/10.1051/m2an/2022093" aria-label="DOI for “An EMA-conserving, pressure-robust and re-semi-robust method with a robust reconstruction method for Navier-Stokes”" title="10.1051/m2an/2022093">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2108.08355"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">R. 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