Document Zbl 1473.65322

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Simul.</a> <a href="/?q=in%3A464244" title="Articles in this Issue">19, No. 2, 830-845 (2021)</a>. </div> <div class="abstract">Summary: This paper is devoted to a study of nonlinear Robin-type boundary value problems of second-order elliptic partial differential equations. Specifically, nonlinear boundary conditions are modeled by hemivariational inequalities, and the coefficients of the governing equations have a small periodic oscillating structure. We prove that the model problem can be homogenized; i.e., the sequence of solutions weakly converges to a homogenized solution as the periodicity approaches zero. We derive an $O(\epsilon^{1/2})$-order estimate in $H^1$-norm for first-order asymptotic expansions. In particular, we provide an optimal $O(\epsilon)$-order estimate in $L^2$-norm for linear Robin boundary value problems. We analyze the numerical error of the Lagrange finite element method for the model problem and design a numerical experiment to validate the theoretical predictions.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7356312">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%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%3A65N15" title="MSC2020">65N15</a> </td> <td class="space"> Error bounds for boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74M15" title="MSC2020">74M15</a> </td> <td class="space"> Contact in solid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74Q05" title="MSC2020">74Q05</a> </td> <td class="space"> Homogenization in equilibrium problems of solid mechanics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aelliptic+hemivariational+inequality">elliptic hemivariational inequality</a>; <a href="/?q=ut%3Ahomogenization">homogenization</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%3Acontact+problems">contact problems</a>; <a href="/?q=ut%3ARobin+problems">Robin problems</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 1473.65322" data-ciurl="/ci/07356312" data-biburl="/bibtex/07356312.bib" data-amsurl="/amsrefs/07356312.bib" data-xmlurl="/xml/07356312.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07356312.pdf" title="Zbl 1473.65322 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/10.1137/19M1252326" aria-label="DOI for “Asymptotic analysis of nonlinear Robin-type boundary value problems with small periodic structure”" title="10.1137/19M1252326">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1902.01018"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">A. 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