Document Zbl 0466.65059

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Comput.</a> <a href="/?q=in%3A145673" title="Articles in this Issue">36, 35-51 (1981)</a>. </div> <div class="abstract"><div class="scan"> <span> Page: <a class="goto" href="/scans/466/372.gif">−5</a> <a class="goto" href="/scans/466/373.gif">−4</a> <a class="goto" href="/scans/466/374.gif">−3</a> <a class="goto" href="/scans/466/375.gif">−2</a> <a class="goto" href="/scans/466/376.gif">−1</a> <a class="goto" href="/scans/466/377.gif">±0</a> <a class="goto" href="/scans/466/378.gif">+1</a> <a class="goto" href="/scans/466/379.gif">+2</a> <a class="goto" href="/scans/466/380.gif">+3</a> <a class="goto" href="/scans/466/381.gif">+4</a> <a class="goto" href="/scans/466/382.gif">+5</a></span> <a class="scan" href="/scans/466/377.gif">Show Scanned Page</a><br> <img src="/scans/466/377.gif" alt="scan of Zbl 0466.65059" onclick="$(this).siblings('.scan').click();"> </div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A3731279">Cited in <strong>5</strong> Reviews</a></div><div class="clear"><a href="/?q=rf%3A3731279">Cited in <strong>131</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%3A65N22" title="MSC2020">65N22</a> </td> <td class="space"> Numerical solution of discretized equations for boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65H10" title="MSC2020">65H10</a> </td> <td class="space"> Numerical computation of solutions to systems of equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65F10" title="MSC2020">65F10</a> </td> <td class="space"> Iterative numerical methods for linear systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35J65" title="MSC2020">35J65</a> </td> <td class="space"> Nonlinear boundary value problems for linear elliptic equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Alarge+sparse+linear+systems">large sparse linear systems</a>; <a href="/?q=ut%3Afinite+element">finite element</a>; <a href="/?q=ut%3ADirichlet+problem">Dirichlet problem</a>; <a href="/?q=ut%3Amulti-+grid+K-level+iteration+procedure">multi- grid K-level iteration procedure</a>; <a href="/?q=ut%3Amildly+non-linear+second-order+partial+differential+equations">mildly non-linear second-order partial differential equations</a>; <a href="/?q=ut%3ANewton-like+methods">Newton-like methods</a>; <a href="/?q=ut%3Acontinuation+methods">continuation methods</a>; <a href="/?q=ut%3Aquadratic+convergence">quadratic convergence</a>; <a href="/?q=ut%3Anumerical+experiments">numerical experiments</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 0466.65059" data-ciurl="/ci/03731279" data-biburl="/bibtex/03731279.bib" data-amsurl="/amsrefs/03731279.bib" data-xmlurl="/xml/03731279.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/03731279.pdf" title="Zbl 0466.65059 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/10.2307/2007724" aria-label="DOI for “An optimal order process for solving finite element equations”" title="10.2307/2007724">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">N. S. Bakhvalov, ”On the convergence of a relaxation method with natural constraints on the elliptic operator,” Ž. Vyčisl. Mat.i Mat. Fiz., v. 6, 1966, pp. 861-885. · <a href="/0154.41002" class="nowrap">Zbl 0154.41002</a></td> </tr><tr> <td>[2]</td> <td class="space">R. E. Bank & Todd Dupont, ”Analysis of a two-level scheme for solving finite element equations,” Numer. Math. (Submitted.)</td> </tr><tr> <td>[3]</td> <td class="space">James H. Bramble, Discrete methods for parabolic equations with time-dependent coefficients, Numerical methods for partial differential equations (Proc. Adv. Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1978) Publ. Math. Res. Center Univ. Wisconsin, vol. 42, Academic Press, New York-London, 1979, pp. 41 – 52.</td> </tr><tr> <td>[4]</td> <td class="space">J. H. Bramble and S. R. Hilbert, Bounds for a class of linear functionals with applications to Hermite interpolation, Numer. Math. 16 (1970/1971), 362 – 369. · <a href="/0214.41405" class="nowrap">Zbl 0214.41405</a> · <a href="https://doi.org/10.1007/BF02165007" class="nowrap">doi:10.1007/BF02165007</a></td> </tr><tr> <td>[5]</td> <td class="space">James H. Bramble and Miloš Zlámal, Triangular elements in the finite element method, Math. Comp. 24 (1970), 809 – 820. · <a href="/0226.65073" class="nowrap">Zbl 0226.65073</a></td> </tr><tr> <td>[6]</td> <td class="space">Achi Brandt, Multi-level adaptive solutions to boundary-value problems, Math. Comp. 31 (1977), no. 138, 333 – 390. · <a href="/0373.65054" class="nowrap">Zbl 0373.65054</a></td> </tr><tr> <td>[7]</td> <td class="space">Jim Douglas Jr., Todd Dupont, and Richard E. Ewing, Incomplete iteration for time-stepping a Galerkin method for a quasilinear parabolic problem, SIAM J. Numer. Anal. 16 (1979), no. 3, 503 – 522. · <a href="/0411.65064" class="nowrap">Zbl 0411.65064</a> · <a href="https://doi.org/10.1137/0716039" class="nowrap">doi:10.1137/0716039</a></td> </tr><tr> <td>[8]</td> <td class="space">Jim Douglas Jr. and Todd Dupont, Galerkin methods for parabolic equations, SIAM J. Numer. Anal. 7 (1970), 575 – 626. · <a href="/0224.35048" class="nowrap">Zbl 0224.35048</a> · <a href="https://doi.org/10.1137/0707048" class="nowrap">doi:10.1137/0707048</a></td> </tr><tr> <td>[9]</td> <td class="space">Jim Douglas Jr., Effective time-stepping methods for the numerical solution of nonlinear parabolic problems, Mathematics of finite elements and applications, III (Proc. Third MAFELAP Conf., Brunel Univ., Uxbridge, 1978) Academic Press, London-New York, 1979, pp. 289 – 304.</td> </tr><tr> <td>[10]</td> <td class="space">Todd Dupont and Ridgway Scott, Polynomial approximation of functions in Sobolev spaces, Math. Comp. 34 (1980), no. 150, 441 – 463. · <a href="/0423.65009" class="nowrap">Zbl 0423.65009</a></td> </tr><tr> <td>[11]</td> <td class="space">R. P. Fedorenko, A relaxation method of solution of elliptic difference equations, Ž. Vyčisl. Mat. i Mat. Fiz. 1 (1961), 922 – 927 (Russian).</td> </tr><tr> <td>[12]</td> <td class="space">R. P. Fedorenko, On the speed of convergence of an iteration process, Ž. Vyčisl. Mat. i Mat. Fiz. 4 (1964), 559 – 564 (Russian).</td> </tr><tr> <td>[13]</td> <td class="space">Pierre Grisvard, Behavior of the solutions of an elliptic boundary value problem in a polygonal or polyhedral domain, Numerical solution of partial differential equations, III (Proc. Third Sympos. (SYNSPADE), Univ. Maryland, College Park, Md., 1975) Academic Press, New York, 1976, pp. 207 – 274.</td> </tr><tr> <td>[14]</td> <td class="space">W. Hackbusch, On the Convergence of a Multi-Grid Iteration Applied to Finite Element Equations, Report 77-8, Universität zu Köln, July 1977.</td> </tr><tr> <td>[15]</td> <td class="space">W. Hackbusch, On the Computation of Approximate Eigenvalues and Eigenfunctions of Elliptic Operators by Means of a Multi-Grid Method, Report 77-10, Universität zu Köln, August 1977. · <a href="/0403.65043" class="nowrap">Zbl 0403.65043</a></td> </tr><tr> <td>[16]</td> <td class="space">Pierre Jamet, Estimations d’erreur pour des éléments finis droits presque dégénérés, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. \jname RAIRO Analyse Numérique 10 (1976), no. R-1, 43 – 60 (French, with Loose English summary). · <a href="/0346.65052" class="nowrap">Zbl 0346.65052</a></td> </tr><tr> <td>[17]</td> <td class="space">R. A. Nicolaides, On multiple grid and related techniques for solving discrete elliptic systems, J. Computational Phys. 19 (1975), no. 4, 418 – 431. · <a href="/0363.65081" class="nowrap">Zbl 0363.65081</a></td> </tr><tr> <td>[18]</td> <td class="space">R. A. Nicolaides, On the \?&sup2; convergence of an algorithm for solving finite element equations, Math. Comp. 31 (1977), no. 140, 892 – 906. · <a href="/0384.65052" class="nowrap">Zbl 0384.65052</a></td> </tr><tr> <td>[19]</td> <td class="space">Donald J. Rose and Gregory F. Whitten, A recursive analysis of dissection strategies, Sparse matrix computations (Proc. Sympos., Argonne Nat. Lab., Lemont, Ill., 1975) Academic Press, New York, 1976, pp. 59 – 83. · <a href="/0356.65032" class="nowrap">Zbl 0356.65032</a></td> </tr><tr> <td>[20]</td> <td class="space">Ridgway Scott, Interpolated boundary conditions in the finite element method, SIAM J. Numer. Anal. 12 (1975), 404 – 427. · <a href="/0357.65082" class="nowrap">Zbl 0357.65082</a> · <a href="https://doi.org/10.1137/0712032" class="nowrap">doi:10.1137/0712032</a></td> </tr><tr> <td>[21]</td> <td class="space">Gilbert Strang and George J. Fix, An analysis of the finite element method, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1973. Prentice-Hall Series in Automatic Computation. · <a href="/0356.65096" class="nowrap">Zbl 0356.65096</a></td> </tr><tr> <td>[22]</td> <td class="space">Vidar Thomée, Negative norm estimates and superconvergence in Galerkin methods for parabolic problems, Math. Comp. 34 (1980), no. 149, 93 – 113. · <a href="/0454.65077" class="nowrap">Zbl 0454.65077</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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