Document Zbl 1459.76088

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Comput. Appl. Math.</a> <a href="/?q=in%3A435983" title="Articles in this Issue">363, 35-52 (2020)</a>. </div> <div class="abstract">Summary: The flow arising in arteriosclerosis is modeled by the incompressible flow with a slip boundary condition of friction type in this paper, whose weak solution satisfies a variational inequality. We develop and analyze the stabilized mixed finite volume methods for the resulting model. We first achieve the same optimal order results of the finite volume methods as those of the corresponding finite element methods under the same regularity on the exact solution and a slightly additional regularity on the source term. Also, a super-close result between the respective solutions of the finite element methods and finite volume methods is derived for the first time. For adaptivity, we further derive a posterior estimate for the present problem satisfying the variational inequality, which reduces the computational cost substantially and provides efficient error control for the solution. Finally, numerical results are shown to support the developed convergence theory.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7085957">Cited in <strong>8</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A76M12" title="MSC2020">76M12</a> </td> <td class="space"> Finite volume methods applied to problems in fluid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76Z05" title="MSC2020">76Z05</a> </td> <td class="space"> Physiological flows </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76D07" title="MSC2020">76D07</a> </td> <td class="space"> Stokes and related (Oseen, etc.) flows </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76M30" title="MSC2020">76M30</a> </td> <td class="space"> Variational methods applied to problems in fluid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A92C35" title="MSC2020">92C35</a> </td> <td class="space"> Physiological flow </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AStokes+problem">Stokes problem</a>; <a href="/?q=ut%3Avariational+inequality">variational inequality</a>; <a href="/?q=ut%3Aconvergence">convergence</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 1459.76088" data-ciurl="/ci/07085957" data-biburl="/bibtex/07085957.bib" data-amsurl="/amsrefs/07085957.bib" data-xmlurl="/xml/07085957.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07085957.pdf" title="Zbl 1459.76088 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.cam.2019.05.006" aria-label="DOI for “A priori and a posteriori estimates of stabilized mixed finite volume methods for the incompressible flow arising in arteriosclerosis”" title="10.1016/j.cam.2019.05.006">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">Chen, Z., Finite Element Methods and their Applications (2005), Springer-Verlag: Springer-Verlag Heidelberg and New York · <a href="/1082.65118" class="nowrap">Zbl 1082.65118</a></td> </tr><tr> <td>[2]</td> <td class="space">Ciarlet, P. 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