Document Zbl 1447.65091

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The LPS preserves the stability of the solution and it does not require other stabilization terms as SUPG. The governing equations are designed within a conservative arbitrary Lagrangian-Eulerian (ALE) formulation. The stability and convergence estimates are shown. An optimal order error estimate with conservative ALE formulation and dG in time-dependent domains is derived. The order of convergence with LPS and dG discretization, the effect of the ALE mapping and unconditional stable estimates with LPS and dG are validated using test cases; a unit square which expands and contracts periodically, a spatial dependent convective velocity with interior layers in an expanding and shrinking domain and a convection dominated problem.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A12390">Bülent Karasözen (Ankara)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7209370">Cited in <strong>2</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%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%3A35Q35" title="MSC2020">35Q35</a> </td> <td class="space"> PDEs in connection with fluid mechanics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aconvection-diffusion-reaction+equation">convection-diffusion-reaction equation</a>; <a href="/?q=ut%3Alocal+projection+stabilization">local projection stabilization</a>; <a href="/?q=ut%3Adiscontinuous+Galerkin+method+in+time">discontinuous Galerkin method in time</a>; <a href="/?q=ut%3Aarbitrary+Lagrangian+Eulerian+formulations">arbitrary Lagrangian Eulerian formulations</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 1447.65091" data-ciurl="/ci/07209370" data-biburl="/bibtex/07209370.bib" data-amsurl="/amsrefs/07209370.bib" data-xmlurl="/xml/07209370.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07209370.pdf" title="Zbl 1447.65091 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/10.1007/s10543-019-00783-2" aria-label="DOI for “Local projection stabilization with discontinuous Galerkin method in time applied to convection dominated problems in time-dependent domains”" title="10.1007/s10543-019-00783-2">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">Ahmed, N.; Matthies, G.; Tobiska, L.; Xie, H., Discontinuous Galerkin time stepping with local projection stabilization for transient convection-diffusion-reaction problems, Comput. 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