Document Zbl 1522.65228

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Comput. Appl. Math.</a> <a href="/?q=in%3A502071" title="Articles in this Issue">436, Article ID 115397, 21 p. (2024)</a>. </div> <div class="abstract">Summary: In this paper, we develop the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with mixed boundary conditions (Dirichlet and Neumann) for the elasticity equations in high contrast media. By a special treatment of mixed boundary conditions separately, and combining the construction of the relaxed and constraint version of the CEM-GMsFEM, we discover that the method offers some advantages such as the independence of the target region’s contrast from precision, while the sizes of oversampling domains have a significant impact on numerical accuracy. Moreover, to our best knowledge, this is the first proof of the convergence of the CEM-GMsFEM with mixed boundary conditions for the elasticity equations given. Some numerical experiments are provided to demonstrate the method’s performance.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7738647">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%3A74B10" title="MSC2020">74B10</a> </td> <td class="space"> Linear elasticity with initial stresses </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74G65" title="MSC2020">74G65</a> </td> <td class="space"> Energy minimization in equilibrium problems in solid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74M25" title="MSC2020">74M25</a> </td> <td class="space"> Micromechanics of solids </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74S05" title="MSC2020">74S05</a> </td> <td class="space"> Finite element methods applied to problems in solid mechanics </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%3ACEM-GMsFEM">CEM-GMsFEM</a>; <a href="/?q=ut%3Amixed+boundary+conditions">mixed boundary conditions</a>; <a href="/?q=ut%3Ahigh+contrast+media">high contrast media</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 1522.65228" data-ciurl="/ci/07738647" data-biburl="/bibtex/07738647.bib" data-amsurl="/amsrefs/07738647.bib" data-xmlurl="/xml/07738647.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07738647.pdf" title="Zbl 1522.65228 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.2023.115397" aria-label="DOI for “A multiscale method for inhomogeneous elastic problems with high contrast coefficients”" title="10.1016/j.cam.2023.115397">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2210.11297"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">Altawallbeh, Z.; Al-Smadi, M.; Komashynska, I.; Ateiwi, A., Numerical solutions of fractional systems of two-point BVPs by using the iterative reproducing kernel algorithm, Ukr. 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