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The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. <a href="https://mathscinet.ams.org/mathscinet/search/journal/profile?groupId=3285" target="new">Subscribers to MathSciNet</a> may click through for more detailed information. </div> </p> </section> </div> </header> <main> <section class="row"> <nav class="col-md-3">  <nav class="journals-list-group"> <script type="text/javascript" src="/journals/javascript/mcom_nav.js"></script> <a href="/journals/journals"><i class="fa-sharp fa-solid fa-house"></i> Journals Home</a> <a href="/epubsearch">eContent Search</a> <a href="/aboutmcom" class="">About Mathematics of Computation</a> <a href="/mcomedit" class="">Editorial Board</a> <a href="/mcom/mcomsubmit.html" class="">Author and Submission Information</a> <a href="/policies/policies" class="" target="_blank">Journal Policies</a> <a href="/subscriberinfo" class="" target="_blank">Subscription Information</a> <a href="/jemail" class="" target="_blank"> Journal Email Notifications</a> <hr> <a href="/pairing/pair_my_device.html"><i class="fa fa-globe" aria-hidden="true"></i> Remote Access</a> </nav> </nav> <article class="col-md-9"> <section>   <div class="row">  <ul class="nav nav-tabs"> <li role="presentation" class=""> <script type="text/javascript" src="/journals/javascript/mcom_nav.js"></script> <a href="javascript: goto_most_recent_mcom()" aria-controls="currissue" role="tab"> Current volume </a> </li> <li role="presentation" class="">  <a href="/cgi-bin/mstrack/accepted_papers/mcom?active=press" aria-controls="press" role="tab">Articles in press </a> </li> <li role="presentation" class=""> <a href="/journals/mcom/0000-000-00?active=recent"> Recently published</a> </li> <li role="presentation" class=""> <a href="/journals/mcom/all_issues.html?active=allissues"> All issues : 1943 – Present </a> </li> </ul> <script src="/js/abstracts/ajaxcall.js"></script> </div> <p> </p> <style> #navCell { display: none;} </style> <script src="/journals/javascript/references.js" type="text/javascript"></script> <script async src="/js/mj.js"></script>  <script src="https://platform-api.sharethis.com/js/sharethis.js#property=598c93d1e2587a001253a011&product=unknown" async="async"></script>  <div class="sharethis-inline-share-buttons"></div>   <article class="col-md-12"> <header> <h2>Superconvergence of quadratic finite elements on mildly structured grids<br> <small>HTML articles powered by AMS MathViewer <a href="/AMSMathViewer"><i class="fa fa-info-circle" aria-label="about MathViewer"></i></a></small></h2> <dl> <dd>by <a href="https://mathscinet.ams.org/mathscinet/search/authors.html?authorName=Huang%2C%20Yunqing">Yunqing Huang</a> and <a href="https://mathscinet.ams.org/mathscinet/search/authors.html?mrauthid=228866">Jinchao Xu</a>;  </dd> <dd>Math. Comp. <strong>77</strong> (2008), 1253-1268 </dd> <dd> DOI: https://doi.org/10.1090/S0025-5718-08-02051-6 </dd> <dd> Published electronically: March 4, 2008 </dd> <dd class="mathviewerPDFLink"> <a href="S0025-5718-08-02051-6.pdf"><small>PDF</small></a> | <a href="https://www.copyright.com/openurl.do?issn=1088-6842&WT.mc.it=American%20Mathematical%20Society" target="_blank">Request permission</a> </dd> </dl> </header> <section id="Abstract"> <h2>Abstract:</h2> Superconvergence estimates are studied in this paper on quadratic finite element discretizations for second order elliptic boundary value problems on mildly structured triangular meshes. For a large class of practically useful grids, the finite element solution $u_h$ is proven to be superclose to the interpolant $u_I$ and as a result a postprocessing gradient recovery scheme for $u_h$ can be devised. The analysis is based on a number of carefully derived identities. In addition to its own theoretical interests, the result in this paper can be used for deriving asymptotically exact a posteriori error estimators for quadratic finite element methods. </section> <section id="references"> <details> <summary>References</summary> <ul><li><a href="https://mathscinet.ams.org/mathscinet/search/authors.html?authorName=Andreev%2C%20A.%20B.">A. B. Andreev</a>, <em>Error estimate of type superconvergence of the gradient for quadratic triangular elements</em>, C. R. Acad. Bulgare Sci. <strong>37</strong> (1984), no. 9, 1179–1182. <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=779566">MR <strong>779566</strong></a></li> <li><a href="https://mathscinet.ams.org/mathscinet/search/authors.html?authorName=Andreev%2C%20A.%20B.">A. B. Andreev</a> and <a href="https://mathscinet.ams.org/mathscinet/search/authors.html?authorName=Lazarov%2C%20Raico%20D.">Raičo D. Lazarov</a>, <em>Superconvergence of the gradient for quadratic triangular finite elements</em>, Numer. Methods Partial Differential Equations <strong>4</strong> (1988), no. 1, 15–32. <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=1012472">MR <strong>1012472</strong></a>, DOI <a href="https://doi.org/10.1002/num.1690040103">10.1002/num.1690040103</a></li> <li> I. Babuska and W. Rheinboldt. A posteriori error estimates for the finite element method. <em>Internat. J. Numer. 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Finite element superconvergence theory. <em>Hunan Science Press</em>, 1989. </ul> </details> </section> <section id="similar"> <details> <summary>Similar Articles</summary> <ul> <li> Retrieve articles in <em>Mathematics of Computation</em> with MSC (2000): <a href="/joursearch/servlet/DoSearch?f1=msc&v1=65N50&jrnl=one&onejrnl=mcom">65N50</a>, <a href="/joursearch/servlet/DoSearch?f1=msc&v1=65N30&jrnl=one&onejrnl=mcom">65N30</a> </li> <li> Retrieve articles in all journals with MSC (2000): <a href="/joursearch/servlet/DoSearch?f1=msc&v1=65N50">65N50</a>, <a href="/joursearch/servlet/DoSearch?f1=msc&v1=65N30">65N30</a> </ul> </details> </section> <section id="additionalinformation"> <details open> <summary>Bibliographic Information</summary> <ul> <li><strong>Yunqing Huang</strong></li><li>Affiliation: Institute for Computational and Applied Mathematics and Hunan Key Laboratory for Computation & Simulation in Science & Engineering, Xiangtan University, People’s Republic of China, 411105</li> <li>Email: huangyq@xtu.edu.cn</li> <li><strong>Jinchao Xu</strong></li><li>Affiliation: Institute for Computational and Applied Mathematics, Xiangtan University, People’s Republic of China and Center for Computational Mathematics and Applications, Pennsylvania State University, USA</li> <li>MR Author ID: <a href='https://mathscinet.ams.org/mathscinet/search/authors.html?mrauthid=228866'>228866</a></li><li>Email: xu@math.psu.edu</li> <li>Received by editor(s): February 2, 2006</li> <li>Received by editor(s) in revised form: March 2, 2007</li> <li>Published electronically: March 4, 2008</li> <li>Additional Notes: The work of the first author was supported in part by the NSFC for Distinguished Young Scholars (10625106) and the National Basic Research Program of China under the grant 2005CB321701<br /> The second author was supported in part by the Furong Scholar Program of Hunan Province through Xiangtan University</li> <li>© Copyright 2008 American Mathematical Society <br />The copyright for this article reverts to public domain 28 years after publication.</li> <li>Journal: Math. Comp. <strong>77</strong> (2008), 1253-1268 </li> <li>MSC (2000): Primary 65N50, 65N30 <li>DOI: https://doi.org/10.1090/S0025-5718-08-02051-6</li> <li>MathSciNet review: <a href = "https://mathscinet.ams.org/mathscinet-getitem?mr=2398767">2398767</a></li> </ul> </details> </section> </article> </section> </article> </section> </main> </div>   <hr class="mx-auto"> <footer id="pagefooter" class="text-center"> <div class="container text-center"> <div class="row">  <div class="col-12 mb-1"> <p> American Mathematical Society · <a href="https://goo.gl/maps/ZvJdkQEC79p" title="Google map 201 Charles Street Providence, Rhode Island" aria-label="Google map to AMS headquarters"> 201 Charles Street Providence, Rhode Island 02904-2213 </a> · <a href="/reach" aria-label="Contact Us">Contact Us</a> </p> </div>  <script src="https://kit.fontawesome.com/2ad6d7fbd6.js" crossorigin="anonymous" defer></script>  <nav class="col-12 mb-1" aria-label="Social media links"> <ul class="list-inline"> <li class="list-inline-item"> <a href="https://www.facebook.com/amermathsoc" class="link-dark" title="Follow us on Facebook" aria-label="View the AMS on Facebook"> <i class="fa-brands fa-facebook-f" aria-hidden="true"></i></a></li> <li class="list-inline-item"> <a href="https://bsky.app/profile/amermathsoc.bsky.social" class="link-dark" title="Follow us on Bluesky" aria-label="View the AMS on Bluesky"> <i class="fa-brands fa-bluesky"></i></a></li> <li class="list-inline-item"> <a href="https://twitter.com/amermathsoc" class="link-dark" title="Follow us on X" aria-label="View the AMS on X"> <i class="fa-brands fa-x-twitter" aria-hidden="true"></i></a></li> <li class="list-inline-item"> <a href="https://www.linkedin.com/company/51001" class="link-dark" title="Follow us on LinkedIn" aria-label="View the AMS on LinkedIn"> <i class="fa-brands fa-linkedin-in" aria-hidden="true"></i></a></li> <li class="list-inline-item"> <a href="https://www.instagram.com/amermathsoc" class="link-dark" title="Follow us on Instagram" aria-label="View the AMS on Instagram"> <i class="fa-brands fa-instagram" aria-hidden="true"></i></a></li> <li class="list-inline-item"> <a href="https://www.youtube.com/amermathsoc" class="link-dark" title="Follow us on YouTube" aria-label="View the AMS on YouTube"> <i class="fa-brands fa-youtube" aria-hidden="true"></i></a></li> </ul> </nav>  <div class="col-12"> <p><small> © <a href="/copyright" aria-label="Copyright policy">Copyright</a> <span id="copyYear">2024</span> American Mathematical Society · <a href="/privacy" aria-label="Privacy statement">View Our Privacy Statement</a> · <a href="/tou" aria-label="Terms of use">Terms of Use</a> · <a href="/accessibility" aria-label="Accessibility policy">Accessibility and AMS Online Content</a> </small></p> <p><small> AMS, American Mathematical Society, the tri-colored AMS logo, and Advancing research, Creating connections, are trademarks and service marks of the American Mathematical Society and registered in the U.S. Patent and Trademark Office. </small></p> </div> </div> </div> <script> // Dynamically update the copyright year document.getElementById('copyYear').textContent = new Date().getFullYear(); </script> </footer>