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<article article-type="research-article" dtd-version="1.3" xml:lang="ru">
  <front xmlns:xlink="http://www.w3.org/1999/xlink">
    <journal-meta>
      <journal-title-group>
        <journal-title>St. Petersburg Polytechnic University Journal: Physics and Mathematics</journal-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Научно-технические ведомости СПбГПУ. Физико-математические науки</trans-title>
        </trans-title-group>
      </journal-title-group>
      <issn pub-type="epub">2304-9782, 2618-8686, 2405-7223</issn>
    </journal-meta>
    <article-meta xmlns:xlink="http://www.w3.org/1999/xlink">
      <article-id pub-id-type="publisher-id">11</article-id>
      <article-id pub-id-type="doi">10.18721/JPM.12111</article-id>
      <title-group>
        <article-title>A posteriori error estimate for Reissner – Mindlin plates: verification of implementations and numerical testing</article-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Вычислительный эксперимент и верификация реализаций апостериорной оценки для пластин Рейсснера – Миндлина</trans-title>
        </trans-title-group>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Kiselev</surname>
            <given-names>Kirill</given-names>
          </name>
          <xref ref-type="aff" rid="aff1"/>
          <email>kvladimirovich10@gmail.com</email>
        </contrib>
        <contrib contrib-type="author">
          <contrib-id contrib-id-type="orcid">0000-0002-1022-0221</contrib-id>
          <name>
            <surname>Frolov</surname>
            <given-names>Maxim</given-names>
          </name>
          <xref ref-type="aff" rid="aff1"/>
          <email>frolov_me@spbstu.ru</email>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Chistiakova</surname>
            <given-names>Olga</given-names>
          </name>
          <xref ref-type="aff" rid="aff1"/>
          <email>Chistiakova.Olga@gmail.com</email>
        </contrib>
      </contrib-group>
      <aff id="aff1">Peter the Great St. Petersburg Polytechnic University</aff>
      <pub-date publication-format="electronic" date-type="pub" iso-8601-date="2019-03-31">
        <day>31</day>
        <month>03</month>
        <year>2019</year>
      </pub-date>
      <volume>12</volume>
      <issue>1</issue>
      <fpage>128</fpage>
      <lpage>141</lpage>
      <self-uri xmlns:xlink="http://www.w3.org/1999/xlink" content-type="pdf" xlink:href="https://physmath.spbstu.ru/userfiles/files/articles/2019/1/11_128-141_12(1)2019.pdf"/>
      <abstract xml:lang="en">
        <p>A posteriori error estimate for accuracy control of approximate solutions for the problem of Reissner – Mindlin plates bending has been analyzed in the paper. The estimate was constructed using the functional approach based on rigorous mathematical grounds, in particular, on methods of functional analysis. It is valid for all conforming approximations of exact solutions, and therefore, it is robust. The estimate is guaranteed in practical implementations due to reliability of the respective inequality. The above-mentioned properties of the method of error control are very desirable for engineering analysis, where some details of computations might be hidden. Our paper investigated two independent implementations of the estimate. Using specially constructed numerical tests, correctness of both implementation algorithms and similarity of the obtained results for all examples were shown. An overestimation of the true error was established to remain acceptable for a wide range of plate thickness values.</p>
      </abstract>
      <kwd-group xml:lang="en">
        <kwd>a posteriori error estimate</kwd>
        <kwd>finite element method</kwd>
        <kwd>Reissner – Mindlin plate</kwd>
      </kwd-group>
    </article-meta>
  </front>
</article>
