<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-00601723</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-18T06:07:50+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">WAVELET REGULARIZATION OF A FOURIER-GALERKIN METHOD FOR SOLVING THE 2D INCOMPRESSIBLE EULER EQUATIONS</title>
            <author role="aut">
              <persName>
                <forename type="first">Romain</forename>
                <surname>Nguyen van Yen</surname>
              </persName>
              <email type="md5">3b6f7af2132644700f52a1f7a886d4d9</email>
              <email type="domain">sfr.fr</email>
              <idno type="idhal" notation="string">natachanguyen-van-yen</idno>
              <idno type="idhal" notation="numeric">1640813</idno>
              <idno type="halauthorid" notation="string">565929-1640813</idno>
              <idno type="ORCID">https://orcid.org/0009-0007-1348-6192</idno>
              <affiliation ref="#struct-143"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Marie</forename>
                <surname>Farge</surname>
              </persName>
              <idno type="halauthorid">154530-0</idno>
              <affiliation ref="#struct-143"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Kai</forename>
                <surname>Schneider</surname>
              </persName>
              <email type="md5">ed85b5e7b449fb5fbf0883c6a0c9f045</email>
              <email type="domain">univ-amu.fr</email>
              <idno type="idhal" notation="string">kai-schneider</idno>
              <idno type="idhal" notation="numeric">184912</idno>
              <idno type="halauthorid" notation="string">5111-184912</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-1243-6621</idno>
              <idno type="IDREF">https://www.idref.fr/151910391</idno>
              <affiliation ref="#struct-871"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Romain</forename>
                <surname>Nguyen Van Yen</surname>
              </persName>
              <email type="md5">84ebee8d996cc4dd39bdbce00d8a5833</email>
              <email type="domain">zedat.fu-berlin.de</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2011-06-20 12:47:35</date>
              <date type="whenWritten">2009-07-01</date>
              <date type="whenModified">2026-02-07 05:08:58</date>
              <date type="whenReleased">2011-06-20 13:21:11</date>
              <date type="whenProduced">2009-12</date>
              <date type="whenEndEmbargoed">2011-06-20</date>
              <ref type="file" target="https://hal.science/hal-00601723v1/document">
                <date notBefore="2011-06-20"/>
              </ref>
              <ref type="file" subtype="greenPublisher" n="1" target="https://hal.science/hal-00601723v1/file/ESAIM_2009_29.pdf" id="file-601723-27765">
                <date notBefore="2011-06-20"/>
              </ref>
              <ref type="externalLink" target="https://www.esaim-proc.org/articles/proc/pdf/2009/04/proc092907.pdf"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="163156">
                <persName>
                  <forename>Romain</forename>
                  <surname>Nguyen Van Yen</surname>
                </persName>
                <email type="md5">84ebee8d996cc4dd39bdbce00d8a5833</email>
                <email type="domain">zedat.fu-berlin.de</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00601723</idno>
            <idno type="halUri">https://hal.science/hal-00601723</idno>
            <idno type="halBibtex">nguyenvanyen:hal-00601723</idno>
            <idno type="halRefHtml">&lt;i&gt;ESAIM: Proceedings&lt;/i&gt;, 2009, 29, pp.89-107. &lt;a target="_blank" href="https://dx.doi.org/10.1051/proc/2009057"&gt;&amp;#x27E8;10.1051/proc/2009057&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">ESAIM: Proceedings, 2009, 29, pp.89-107. &amp;#x27E8;10.1051/proc/2009057&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-601723-27765"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="INSU">INSU - Institut National des Sciences de l'Univers</idno>
            <idno type="stamp" n="X">École polytechnique</idno>
            <idno type="stamp" n="ENS-PARIS">Ecole Normale Supérieure de Paris</idno>
            <idno type="stamp" n="ENPC" corresp="PARISTECH">École nationale des ponts et chaussées </idno>
            <idno type="stamp" n="UPMC" corresp="SORBONNE-UNIVERSITE">Université Pierre et Marie Curie</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-AMU">Aix Marseille Université</idno>
            <idno type="stamp" n="X-LMD" corresp="X">Laboratoire de Météorologie Dynamique (LMD)</idno>
            <idno type="stamp" n="X-DEP-MECA">Département de mécanique de l’École polytechnique </idno>
            <idno type="stamp" n="PARISTECH">ParisTech</idno>
            <idno type="stamp" n="LMD" corresp="ENS-PARIS">Laboratoire de Météorologie Dynamique</idno>
            <idno type="stamp" n="ENPC-LMD" corresp="ENPC">Laboratoire de Météorologie Dynamique</idno>
            <idno type="stamp" n="M2P2">Mécanique Modélisation et Procédés Propres</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
            <idno type="stamp" n="PSL">Université Paris sciences et lettres</idno>
            <idno type="stamp" n="UPMC_POLE_3" corresp="UPMC">UPMC Pôle 3</idno>
            <idno type="stamp" n="SORBONNE-UNIVERSITE">Sorbonne Université</idno>
            <idno type="stamp" n="SU-SCIENCES" corresp="SORBONNE-UNIVERSITE">Faculté des Sciences de Sorbonne Université</idno>
            <idno type="stamp" n="ENS-PSL" corresp="PSL">École normale supérieure - PSL</idno>
            <idno type="stamp" n="SU-TI">Sorbonne Université - Texte Intégral</idno>
            <idno type="stamp" n="ALLIANCE-SU"> Alliance Sorbonne Université</idno>
            <idno type="stamp" n="IP-PARIS-DEPARTEMENT-MATHEMATIQUES">Département de Mathèmatiques</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">WAVELET REGULARIZATION OF A FOURIER-GALERKIN METHOD FOR SOLVING THE 2D INCOMPRESSIBLE EULER EQUATIONS</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Romain</forename>
                    <surname>Nguyen van Yen</surname>
                  </persName>
                  <email type="md5">3b6f7af2132644700f52a1f7a886d4d9</email>
                  <email type="domain">sfr.fr</email>
                  <idno type="idhal" notation="string">natachanguyen-van-yen</idno>
                  <idno type="idhal" notation="numeric">1640813</idno>
                  <idno type="halauthorid" notation="string">565929-1640813</idno>
                  <idno type="ORCID">https://orcid.org/0009-0007-1348-6192</idno>
                  <affiliation ref="#struct-143"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Marie</forename>
                    <surname>Farge</surname>
                  </persName>
                  <idno type="halauthorid">154530-0</idno>
                  <affiliation ref="#struct-143"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Kai</forename>
                    <surname>Schneider</surname>
                  </persName>
                  <email type="md5">ed85b5e7b449fb5fbf0883c6a0c9f045</email>
                  <email type="domain">univ-amu.fr</email>
                  <idno type="idhal" notation="string">kai-schneider</idno>
                  <idno type="idhal" notation="numeric">184912</idno>
                  <idno type="halauthorid" notation="string">5111-184912</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-1243-6621</idno>
                  <idno type="IDREF">https://www.idref.fr/151910391</idno>
                  <affiliation ref="#struct-871"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">38939</idno>
                <idno type="issn">1270-900X</idno>
                <title level="j">ESAIM: Proceedings</title>
                <imprint>
                  <publisher>EDP Sciences</publisher>
                  <biblScope unit="volume">29</biblScope>
                  <biblScope unit="pp">89-107</biblScope>
                  <date type="datePub">2009-12</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1051/proc/2009057</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Euler equations</term>
                <term xml:lang="en">Coherent Vorticity Extraction</term>
                <term xml:lang="en">wavelets</term>
              </keywords>
              <classCode scheme="halDomain" n="math.math-na">Mathematics [math]/Numerical Analysis [math.NA]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We employ a Fourier-Galerkin method to solve the 2D incompressible Euler equations, and study several ways to regularize the solution by wavelet ﬁltering at each timestep. Real-valued orthogonal wavelets and complex-valued wavelets are considered, combined with either linear or non-linear ﬁltering. The results are compared with those obtained via classical viscous and hyperviscous regularization methods. Wavelet regularization using complex-valued wavelets performs as well in terms of L2 convergence rate to the reference solution. The compression rate for homogeneous 2D turbulence is around 3 for this method, suggesting that memory and CPU time could be reduced in an adaptive wavelet computation. Our results also suggest L2 convergence to the reference solution without any regularization, in contrast to what is obtained for the 1D Burgers equation.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-143" status="OLD">
          <idno type="RNSR">199812867Z</idno>
          <orgName>Laboratoire de Météorologie Dynamique (UMR 8539)</orgName>
          <orgName type="acronym">LMD</orgName>
          <date type="start">1968-03-29</date>
          <date type="end">1997-12-31</date>
          <desc>
            <address>
              <addrLine>LMD ENS 24 Rue Lhomond 75231 Paris Cedex 05</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.lmd.jussieu.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-93591" type="direct"/>
            <relation active="#struct-300045" type="direct"/>
            <relation active="#struct-300340" type="direct"/>
            <relation active="#struct-563936" type="indirect"/>
            <relation active="#struct-301545" type="direct"/>
            <relation name="UPR1211" active="#struct-441569" type="direct"/>
            <relation active="#struct-506084" type="direct"/>
            <relation active="#struct-59704" type="indirect"/>
            <relation active="#struct-564132" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-871" status="OLD">
          <orgName>Modélisation et Simulation Numérique (en mécanique des fluides)</orgName>
          <orgName type="acronym">M2P2</orgName>
          <date type="start">2004-01-01</date>
          <date type="end">2011-12-31</date>
          <desc>
            <address>
              <addrLine>Technopole de Château-Gombert 38 rue Frédéric Joliot Curie 13451 MARSEILLE CEDEX 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www-msnm.univ-mrs.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-5033" type="direct"/>
            <relation active="#struct-27501" type="direct"/>
            <relation active="#struct-92823" type="direct"/>
            <relation name="UMR6181 / FRE2405" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-93591" status="OLD">
          <idno type="ROR">https://ror.org/02en5vm52</idno>
          <orgName>Université Pierre et Marie Curie - Paris 6</orgName>
          <orgName type="acronym">UPMC</orgName>
          <date type="end">2017-12-31</date>
          <desc>
            <address>
              <addrLine>4 place Jussieu - 75005 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.upmc.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300045" status="VALID">
          <idno type="IdRef">029349265</idno>
          <idno type="ISNI">0000 0001 2154 1736</idno>
          <idno type="ROR">https://ror.org/04kdfz702</idno>
          <idno type="Wikidata">Q3152437</idno>
          <orgName>Institut national des sciences de l'Univers</orgName>
          <orgName type="acronym">INSU - CNRS</orgName>
          <date type="start">2007-04-19</date>
          <desc>
            <address>
              <addrLine>INSU-CNRS3 rue Michel-Ange, 75794 Paris Cedex 16</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.insu.cnrs.fr</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300340" status="VALID">
          <idno type="IdRef">027309320</idno>
          <idno type="ISNI">0000000121581279</idno>
          <idno type="ROR">https://ror.org/05hy3tk52</idno>
          <idno type="Wikidata">Q273626</idno>
          <orgName>École polytechnique</orgName>
          <orgName type="acronym">X</orgName>
          <date type="start">1794-03-11</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91128 Palaiseau Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.polytechnique.edu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-563936" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-563936" status="VALID">
          <idno type="IdRef">238327159</idno>
          <idno type="ISNI">0000000502717600</idno>
          <idno type="ROR">https://ror.org/042tfbd02</idno>
          <idno type="Wikidata">Q48759778</idno>
          <orgName>Institut Polytechnique de Paris</orgName>
          <orgName type="acronym">IP Paris</orgName>
          <date type="start">2019-06-02</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91120 Palaiseau Cedex, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ip-paris.fr</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-301545" status="OLD">
          <idno type="ROR">https://ror.org/02nwvxz07</idno>
          <orgName>École nationale des ponts et chaussées</orgName>
          <orgName type="acronym">ENPC</orgName>
          <date type="start">1747-02-14</date>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>École nationale des ponts et chaussées, 6-8 avenue Blaise-Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://ecoledesponts.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="regrouplaboratory" xml:id="struct-506084" status="VALID">
          <orgName>Département des Géosciences - ENS-PSL</orgName>
          <date type="start">1991-01-01</date>
          <desc>
            <address>
              <addrLine>24 rue Lhomond, 75005 Paris, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.geosciences.ens.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-59704" type="direct"/>
            <relation active="#struct-564132" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-59704" status="VALID">
          <idno type="IdRef">031738419</idno>
          <idno type="ISNI">0000000123532622</idno>
          <idno type="ROR">https://ror.org/05a0dhs15</idno>
          <orgName>École normale supérieure - Paris</orgName>
          <orgName type="acronym">ENS-PSL</orgName>
          <date type="start">1985-07-24</date>
          <desc>
            <address>
              <addrLine>45, Rue d'Ulm - 75230 Paris cedex 05</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ens.psl.eu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-564132" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-564132" status="VALID">
          <idno type="IdRef">241597595</idno>
          <idno type="ISNI">0000 0004 1784 3645</idno>
          <idno type="ROR">https://ror.org/013cjyk83</idno>
          <orgName>Université Paris Sciences et Lettres</orgName>
          <orgName type="acronym">PSL</orgName>
          <desc>
            <address>
              <addrLine>60 rue Mazarine 75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.psl.eu/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-5033" status="OLD">
          <idno type="IdRef">026402882</idno>
          <orgName>Université de la Méditerranée - Aix-Marseille 2</orgName>
          <date type="start">1969</date>
          <date type="end">2011</date>
          <desc>
            <address>
              <addrLine>58, boulevard Charles Livon - 13284 Marseille cedex 07</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univmed.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-27501" status="OLD">
          <idno type="IdRef">026403153</idno>
          <orgName>Université Paul Cézanne - Aix-Marseille 3</orgName>
          <date type="end">2011</date>
          <desc>
            <address>
              <addrLine>3, avenue Robert Schumann - 13628 Aix-en-Provence cedex 1</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-cezanne.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-92823" status="OLD">
          <idno type="IdRef">026403781</idno>
          <orgName>Université de Provence - Aix-Marseille 1</orgName>
          <date type="end">2011-12-31</date>
          <desc>
            <address>
              <addrLine>3, place Victor Hugo - 13331 Marseille Cedex 03</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-provence.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>