<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"       "http://www.w3.org/TR/REC-html40/loose.dtd">  <HTML> <HEAD><TITLE>RR-4505 : Stabilit&eacute; des m&eacute;thodes de Lagrange-Galerkin du premier et du second ordre </TITLE> <link rel="stylesheet" href="/css/pagestrict.css"> <link rel="stylesheet" href="/css/pagefinalestrict.css"> <META NAME="code" CONTENT="CAIMAN">  <META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1"> <META NAME="description" CONTENT="Fourestey, Gilles"> <META NAME="dc.title" CONTENT="Stabilit&eacute; des m&eacute;thodes de Lagrange-Galerkin du premier et du second ordre"> <META NAME="dc.creator" CONTENT="Fourestey, Gilles"> <META NAME="dc.subject" CONTENT="METHODE DE LAGRANGE-GALERKIN; ORDRE ELEVE; STABILITE; LAGRANGE-GALERGIN METHOD; HIGH ORDRE; STABILITY"> <META NAME="dc.description" CONTENT="Fourestey, Gilles"> <META NAME="dc.publisher" CONTENT="INRIA"> <META NAME="dc.date" CONTENT="(SCHEME=ISO8601) 2002-07"> <META NAME="dc.identifier" CONTENT="(SCHEME=ISRN) ISRN INRIA/RR--4505--FR"> <META NAME="dc.type" CONTENT="Text.TechReport"> <META NAME="dc.language" CONTENT="(SCHEME=ISO639-1) fr"> <STYLE TYPE="text/css"> <!-- #Etiquette { visibility: visible } #UrFenetre  { position:absolute; 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des m&eacute;thodes de Lagrange-Galerkin du premier et du second ordre <BR>  <img src="../images/ti_dessous.gif" width="329" height="18" alt="-----------------------">  </h1> <BLOCKQUOTE> <FONT SIZE="4"><DIV ID="Etiquette"><A HREF="http://indexation.inria.fr:8080/cgi-bin/query?mss=RRRT%2Fsimple&pg=q&what=web&enc=iso88591&q=dc.creator%3DFourestey%2CGilles+url%3Ahttp%3A%2F%2Fwww.inria.fr%2Frrrt%2F&q1=dc.creator%3DFourestey%2CGilles&searchrrrt=Chercher"ONMOUSEOVER="MM_showHideLayers('document.layers[\'Etiquette2\']','document.all[\'Etiquette2\']','show','document.layers[\'AuteurFenetre\']','document.all[\'AuteurFenetre\']','show')" ONMOUSEOUT="MM_showHideLayers('document.layers[\'AuteurFenetre\']','document.all[\'AuteurFenetre\']','hide','document.layers[\'Etiquette2\']','document.all[\'Etiquette2\']','hide')"<!--div class=aut-->Fourestey, Gilles<!--/div--></A> </FONT></DIV><BR><DIV ID="AuteurFenetre"> <table border=6> <TR><TD bgcolor="#215E21">  <font color="#FFFFFF">Les rapports de cet auteur</font> </TD></TR></table></DIV> <DIV ID="Etiquette">Rapport de recherche de l'INRIA-<A HREF="/inria/organigramme/fiche_ur-sop.fr.html" target="d"ONMOUSEOVER="MM_showHideLayers('document.layers[\'Etiquette2\']','document.all[\'Etiquette2\']','show','document.layers[\'UrFenetre\']','document.all[\'UrFenetre\']','show')" ONMOUSEOUT="MM_showHideLayers('document.layers[\'UrFenetre\']','document.all[\'UrFenetre\']','hide','document.layers[\'Etiquette2\']','document.all[\'Etiquette2\']','hide')"> Sophia Antipolis</A></DIV>  <DIV ID="UrFenetre"><table border=6><TR><TD bgcolor="#215E21">  <font color="#FFFFFF"> Page d'accueil de l'unit de recherche</font> </TD></TR></table></DIV><P><P> <!--qqps--><DIV ID="Etiquette"><A HREF="ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-4505.ps.gz"ONMOUSEOVER="MM_showHideLayers('document.layers[\'Etiquette2\']','document.all[\'Etiquette2\']','show','document.layers[\'PsFenetre\']','document.all[\'PsFenetre\']','show')" ONMOUSEOUT="MM_showHideLayers('document.layers[\'PsFenetre\']','document.all[\'PsFenetre\']','hide','document.layers[\'Etiquette2\']','document.all[\'Etiquette2\']','hide')">Fichier PostScript / <em>PostScript file</em></A></DIV> <DIV ID="PsFenetre"><table border=6> <TR><TD bgcolor="#215E21"> <font color="#FFFFFF">Fichier postscript du document :<BR>1494 Ko </font></TD></TR></table></DIV><P> <!--qqpdf--><DIV ID="Etiquette"><A HREF="ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4505.pdf "ONMOUSEOVER="MM_showHideLayers('document.layers[\'Etiquette2\']','document.all[\'Etiquette2\']','show','document.layers[\'PdfFenetre\']','document.all[\'PdfFenetre\']','show')" ONMOUSEOUT="MM_showHideLayers('document.layers[\'PdfFenetre\']','document.all[\'PdfFenetre\']','hide','document.layers[\'Etiquette2\']','document.all[\'Etiquette2\']','hide')">Fichier PDF / <em>PDF file</em></A></DIV> <DIV ID="PdfFenetre"><table border=6> <TR><TD bgcolor="#215E21"> <font color="#FFFFFF">Fichier PDF du document :<BR>3667 Ko </font></TD></TR></table></DIV><P><DIV ID="Etiquette"><A HREF="../recherche/equipes/caiman.fr.html" target="d"ONMOUSEOVER="MM_showHideLayers('document.layers[\'Etiquette2\']','document.all[\'Etiquette2\']','show','document.layers[\'ProjetFenetre\']','document.all[\'ProjetFenetre\']','show')" ONMOUSEOUT="MM_showHideLayers('document.layers[\'ProjetFenetre\']','document.all[\'ProjetFenetre\']','hide','document.layers[\'Etiquette2\']','document.all[\'Etiquette2\']','hide')">Projet : CAIMAN</A> -  38 pages - Juillet 2002 - Document en franais </DIV> <DIV ID="ProjetFenetre"> <table border=6> <TR><TD bgcolor="#215E21">  <font color="#FFFFFF">Page d'accueil du projet</font> </TD></TR></table></DIV><P><em>Titre anglais : Stability of the first and second order Lagrange-Galerkin methods</em><HR>Abstract :  The Lagrange-Galerkin method, which allows for example the resolution of an advection equation, is based upon the characteristics method coupled with a finite element formulation. Its stability has been thouroughly studied with a first-order time-accurate scheme and has shown a non-linear instability when a non-exact integration is used when computing the inner products. We propose in this report a similar study when a second-order time-accurate Lagrange-Galerkin method is used. <P> <em>R&eacute;sum&eacute : La m&eacute;thode de Lagrange-Galerkin, qui permet de r&eacute;soudre par exemple l'&eacute;quation d'advection, est bas&eacute;e sur l'utilisation de la m&eacute;thode des caract&eacute;ristiques coupl&eacute;e &agrave; une formulation de type &eacute;l&eacute;ments finis. La plupart des &eacute;tudes concernant la stabilit&eacute; de cette m&eacute;thode font intervenir une formulation du premier ordre en temps et montrent qu'en cas d'int&eacute;gration non exacte des produits internes, le sch&eacute;ma obtenu induit des instabilit&eacute;s non lin&eacute;aires. Nous proposons, dans ce rapport, une &eacute;tude de ces m&ecirc;mes instabilit&eacute;s pour une formulation de Lagrange-Galerkin d'ordre deux en temps. </em><P><HR>KEY-WORDS : LAGRANGE-GALERGIN METHOD / HIGH ORDRE / STABILITY<P>MOTS-CLES : M&Eacute;THODE DE LAGRANGE-GALERKIN / ORDRE &Eacute;LEV&Eacute; / STABILIT&Eacute;<P> <HR> </BLOCKQUOTE> </BODY> </HTML> 
