Document Zbl 1518.65107

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Sci. Comput.</a> <a href="/?q=in%3A498225" title="Articles in this Issue">96, No. 1, Paper No. 3, 28 p. (2023)</a>. </div> <div class="abstract">Summary: A fully discrete finite element scheme is proposed to solve the dynamic viscoelastic contact problem with multi-contact zones and unilateral constraints. We develop the well-posedness and error analysis of the nonlinear numerical scheme under appropriate assumptions on the regularity of the solution. Moreover, we provide a projection-iteration algorithm for computation and show the convergence. Several numerical experiments are carried out to validate the theoretical results.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7698874">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%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%3A74H15" title="MSC2020">74H15</a> </td> <td class="space"> Numerical approximation of solutions of dynamical problems in solid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74D10" title="MSC2020">74D10</a> </td> <td class="space"> Nonlinear constitutive equations for materials with memory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35A01" title="MSC2020">35A01</a> </td> <td class="space"> Existence problems for PDEs: global existence, local existence, non-existence </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35A02" title="MSC2020">35A02</a> </td> <td class="space"> Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35B65" title="MSC2020">35B65</a> </td> <td class="space"> Smoothness and regularity of solutions to PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35Q74" title="MSC2020">35Q74</a> </td> <td class="space"> PDEs in connection with mechanics of deformable solids </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Adynamic+contact+problem">dynamic contact problem</a>; <a href="/?q=ut%3Amulti-contact+zones">multi-contact zones</a>; <a href="/?q=ut%3Afinite+element+method">finite element method</a>; <a href="/?q=ut%3Aerror+estimates">error estimates</a>; <a href="/?q=ut%3Aprojection-iteration+algorithm">projection-iteration algorithm</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 1518.65107" data-ciurl="/ci/07698874" data-biburl="/bibtex/07698874.bib" data-amsurl="/amsrefs/07698874.bib" data-xmlurl="/xml/07698874.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07698874.pdf" title="Zbl 1518.65107 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/s10915-023-02228-z" aria-label="DOI for “A fully-discrete finite element scheme and projection-iteration algorithm for a dynamic contact problem with multi-contact zones and unilateral constraint”" title="10.1007/s10915-023-02228-z">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">Barboteu, M.; 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