Document Zbl 07835989

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<a href="/authors/gusev.alexander-a" title="Author Profile">Gusev, Alexander A.</a><a class="btn btn-default btn-xs matrix" type="button" href="https://donald.zentralblatt-math.org/lethe/recruit/?first_name=Alexander+A.&last_name=Gusev&document_id=7835989"> <span class="text-danger">Recruit</span> </a>; <a href="/authors/deveikis.algirdas" title="Author Profile">Deveikis, Algirdas</a><a class="btn btn-default btn-xs matrix" type="button" href="https://donald.zentralblatt-math.org/lethe/recruit/?first_name=Algirdas&last_name=Deveikis&document_id=7835989"> <span class="text-danger">Recruit</span> </a>; <a href="/authors/chuluunbaatar.galmandakh" title="Author Profile">Chuluunbaatar, Galmandakh</a><a class="btn btn-default btn-xs matrix" type="button" href="https://donald.zentralblatt-math.org/lethe/recruit/?first_name=Galmandakh&last_name=Chuluunbaatar&document_id=7835989"> <span class="text-danger">Recruit</span> </a>; <a href="/authors/ulziibayar.vandandoo" title="Author Profile">Ulziibayar, Vandandoo</a><a class="btn btn-default btn-xs matrix" type="button" href="https://donald.zentralblatt-math.org/lethe/recruit/?first_name=Vandandoo&last_name=Ulziibayar&document_id=7835989"> <span class="text-danger">Recruit</span> </a></div> <h2 class="title"> <strong>Schemes of finite element method for solving multidimensional boundary value problems.</strong> <i>(English)</i> <a class="label nowrap" href="/7835989">Zbl 07835989</a> </h2> <div class="source"> <a href="/serials/1955" title="Journal Profile">J. Math. Sci., New York</a> <a href="/?q=in%3A511341" title="Articles in this Issue">279, No. 6, 738-755 (2024)</a>. </div> <div class="abstract"><div class="pre">Summary: We propose new computational schemes and algorithms of the finite element method for solving elliptic multidimensional boundary value problems with variable coefficients at derivatives in a polyhedral d-dimensional domain, aimed at describing collective models of atomic nuclei. The desired solution is sought in the form of an expansion in the basis of piecewise polynomial functions constructed in an analytical form by joining Hermite interpolation polynomials and their derivatives on the boundaries of neighboring finite elements having the form of d-dimensional parallelepipeds. Calculations of the spectrum, quadrupole momentum and electric transitions of standard boundary value problems for the geometric collective model of atomic nuclei are analyzed.</div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7835989">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65Nxx" title="MSC2020">65Nxx</a> </td> <td class="space"> Numerical methods for partial differential equations, boundary value problems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Acomputational+schemes">computational schemes</a>; <a href="/?q=ut%3Afinite+element+method">finite element method</a>; <a href="/?q=ut%3Aelliptic+multidimensional+boundary+value+problems">elliptic multidimensional boundary value problems</a></div> <div class="software"> <h3>Software:</h3><a href="/software/46067">GCMFEM</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 07835989" data-ciurl="/ci/07835989" data-biburl="/bibtex/07835989.bib" data-amsurl="/amsrefs/07835989.bib" data-xmlurl="/xml/07835989.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07835989.pdf" title="Zbl 07835989 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/s10958-024-07056-6" aria-label="DOI for “Schemes of finite element method for solving multidimensional boundary value problems”" title="10.1007/s10958-024-07056-6">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">K. J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall (1982).</td> </tr><tr> <td>[2]</td> <td class="space">Berezin, IS; Zhidkov, NP, Computing Methods, 1965, Oxford: Pergamon Press, Oxford · <a href="/0122.12903" class="nowrap">Zbl 0122.12903</a></td> </tr><tr> <td>[3]</td> <td class="space">Lorentz, RA, Multivariate Birkhoff interpolation, 1992, Berlin: Springer, Berlin · <a href="/0760.41002" class="nowrap">Zbl 0760.41002</a> · <a href="https://doi.org/10.1007/BFb0088788" class="nowrap">doi:10.1007/BFb0088788</a></td> </tr><tr> <td>[4]</td> <td class="space">Lekien, F.; Marsden, J., Tricubic interpolation in three dimensions, Int. J. Num. Meth. Eng., 63, 455-471, 2005 · <a href="/1140.76423" class="nowrap">Zbl 1140.76423</a> · <a href="https://doi.org/10.1002/nme.1296" class="nowrap">doi:10.1002/nme.1296</a></td> </tr><tr> <td>[5]</td> <td class="space">Vandandoo, U., High-Order Finite Difference and Finite-Element Methods for Solving Some Partial Differential Equations, 2024, Charm: Springer, Charm · <a href="/1542.65003" class="nowrap">Zbl 1542.65003</a> · <a href="https://doi.org/10.1007/978-3-031-44784-6" class="nowrap">doi:10.1007/978-3-031-44784-6</a></td> </tr><tr> <td>[6]</td> <td class="space">G. Chuluunbaatar et al, “Construction of multivariate interpolation Hermite polynomials for finite element method,” EPJ Web of Conferences226, Article No. 02007 (2020).</td> </tr><tr> <td>[7]</td> <td class="space">A. A. Gusev et al, “Hermite interpolation polynomials on parallelepipeds and FEM applications,” Math. Comput. 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Hadrons and Nuclei, 343, 25-34, 1992 · <a href="https://doi.org/10.1007/BF01291593" class="nowrap">doi:10.1007/BF01291593</a></td> </tr><tr> <td>[11]</td> <td class="space">D. Troltenier, J. A. Maruhn, and P. O. Hess, “Numerical application of the geometric collective model,” In: Computational Nuclear Physics. Vol. 1, pp. 105-128, Springer, Berlin (1991).</td> </tr><tr> <td>[12]</td> <td class="space">Deveikis, A., Symbolic-numeric algorithm for calculations in geometric collective model of atomic nuclei, Lect. Notes Comput. Sci., 13366, 103-123, 2022 · <a href="/1517.81098" class="nowrap">Zbl 1517.81098</a> · <a href="https://doi.org/10.1007/978-3-031-14788-3_7" class="nowrap">doi:10.1007/978-3-031-14788-3_7</a></td> </tr><tr> <td>[13]</td> <td class="space">A. Dobrowolski, K. Mazurek, and A. G´o´zd´z, “Rotational bands in the quadrupole-octupole collective model,” Phys. Rev. C97, 024321, 11 p. 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