<?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-04593726</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="2026-05-05T03:14:22+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">The Neumann boundary condition for the two-dimensional Lax-Wendroff scheme. II</title>
            <title xml:lang="fr">La condition au bord de Neumann pour le schéma de Lax-Wendroff bi-dimensionnel. II</title>
            <author role="aut">
              <persName>
                <forename type="first">Antoine</forename>
                <surname>Benoit</surname>
              </persName>
              <email type="md5">d53595ccebc80d2eae721de26202f6de</email>
              <email type="domain">univ-nantes.fr</email>
              <idno type="idhal" notation="string">antoine-benoit</idno>
              <idno type="idhal" notation="numeric">753204</idno>
              <idno type="halauthorid" notation="string">31613-753204</idno>
              <idno type="IDREF">https://www.idref.fr/200035266</idno>
              <idno type="VIAF">https://viaf.org/viaf/221149717622210952513</idno>
              <affiliation ref="#struct-2563"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Jean-François</forename>
                <surname>Coulombel</surname>
              </persName>
              <email type="md5">7c7c919c47204ebbce4c9c1825ae6c86</email>
              <email type="domain">math.univ-toulouse.fr</email>
              <idno type="idhal" notation="string">jean-francois-coulombel</idno>
              <idno type="idhal" notation="numeric">20049</idno>
              <idno type="halauthorid" notation="string">886-20049</idno>
              <idno type="IDREF">https://www.idref.fr/078813506</idno>
              <idno type="ORCID">https://orcid.org/0009-0003-4116-9443</idno>
              <affiliation ref="#struct-1612769"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Jean-François</forename>
                <surname>Coulombel</surname>
              </persName>
              <email type="md5">7c7c919c47204ebbce4c9c1825ae6c86</email>
              <email type="domain">math.univ-toulouse.fr</email>
            </editor>
            <funder ref="#projanr-171158"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2024-05-30 09:30:38</date>
              <date type="whenWritten">2024-05-30</date>
              <date type="whenModified">2026-05-05 03:12:12</date>
              <date type="whenReleased">2024-05-30 10:51:25</date>
              <date type="whenProduced">2025</date>
              <date type="whenEndEmbargoed">2024-05-30</date>
              <ref type="file" target="https://hal.science/hal-04593726v1/document">
                <date notBefore="2024-05-30"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-04593726v1/file/BC2.pdf" id="file-4593726-3986096">
                <date notBefore="2024-05-30"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/2405.19844"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="109430">
                <persName>
                  <forename>Jean-François</forename>
                  <surname>Coulombel</surname>
                </persName>
                <email type="md5">7c7c919c47204ebbce4c9c1825ae6c86</email>
                <email type="domain">math.univ-toulouse.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-04593726</idno>
            <idno type="halUri">https://hal.science/hal-04593726</idno>
            <idno type="halBibtex">benoit:hal-04593726</idno>
            <idno type="halRefHtml">&lt;i&gt;Electronic Transactions on Numerical Analysis&lt;/i&gt;, 2025, 63, pp.320-256. &lt;a target="_blank" href="https://dx.doi.org/10.1553/etna_vol63s320"&gt;&amp;#x27E8;10.1553/etna_vol63s320&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Electronic Transactions on Numerical Analysis, 2025, 63, pp.320-256. &amp;#x27E8;10.1553/etna_vol63s320&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-4593726-3986096"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-TLSE2">Université Toulouse 2</idno>
            <idno type="stamp" n="UNIV-TLSE3">Université de Toulouse</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-LITTORAL">Université du Littoral Côte d'Opale</idno>
            <idno type="stamp" n="INSA-TOULOUSE">Institut National des Sciences Appliquées de Toulouse</idno>
            <idno type="stamp" n="EHESS">Ecole des Hautes Etudes en Sciences Sociales</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="IMT">Institut de Mathématiques de Toulouse</idno>
            <idno type="stamp" n="UT1-CAPITOLE">Université Toulouse 1 Capitole</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="LMPA-JL">Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville</idno>
            <idno type="stamp" n="INSA-GROUPE">Groupe INSA</idno>
            <idno type="stamp" n="INUC">Institut National Universitaire Champollion</idno>
            <idno type="stamp" n="INRAE">Institut National de Recherche en Agriculture, Alimentation et Environnement</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="UNIV-UT3">Université Toulouse 3</idno>
            <idno type="stamp" n="UT3-TOULOUSEINP">Université de Toulouse / Toulouse INP</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">The Neumann boundary condition for the two-dimensional Lax-Wendroff scheme. II</title>
                <title xml:lang="fr">La condition au bord de Neumann pour le schéma de Lax-Wendroff bi-dimensionnel. II</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Antoine</forename>
                    <surname>Benoit</surname>
                  </persName>
                  <email type="md5">d53595ccebc80d2eae721de26202f6de</email>
                  <email type="domain">univ-nantes.fr</email>
                  <idno type="idhal" notation="string">antoine-benoit</idno>
                  <idno type="idhal" notation="numeric">753204</idno>
                  <idno type="halauthorid" notation="string">31613-753204</idno>
                  <idno type="IDREF">https://www.idref.fr/200035266</idno>
                  <idno type="VIAF">https://viaf.org/viaf/221149717622210952513</idno>
                  <affiliation ref="#struct-2563"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Jean-François</forename>
                    <surname>Coulombel</surname>
                  </persName>
                  <email type="md5">7c7c919c47204ebbce4c9c1825ae6c86</email>
                  <email type="domain">math.univ-toulouse.fr</email>
                  <idno type="idhal" notation="string">jean-francois-coulombel</idno>
                  <idno type="idhal" notation="numeric">20049</idno>
                  <idno type="halauthorid" notation="string">886-20049</idno>
                  <idno type="IDREF">https://www.idref.fr/078813506</idno>
                  <idno type="ORCID">https://orcid.org/0009-0003-4116-9443</idno>
                  <affiliation ref="#struct-1612769"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">777</idno>
                <idno type="issn">1068-9613</idno>
                <title level="j">Electronic Transactions on Numerical Analysis</title>
                <imprint>
                  <publisher>Kent State University Library</publisher>
                  <biblScope unit="volume">63</biblScope>
                  <biblScope unit="pp">320-256</biblScope>
                  <date type="datePub">2025</date>
                </imprint>
              </monogr>
              <idno type="arxiv">2405.19844</idno>
              <idno type="doi">10.1553/etna_vol63s320</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">transport equations</term>
                <term xml:lang="en">stability</term>
                <term xml:lang="en">boundary conditions</term>
                <term xml:lang="en">domains with corners</term>
                <term xml:lang="en">numerical schemes</term>
              </keywords>
              <classCode scheme="classification">MSC : 65M12, 65M06, 65M20</classCode>
              <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 study the stability of a two-dimensional Lax-Wendroff scheme in a quarter-plane. Following our previous work, we aim here at adapting the energy method in order to study second order extrapolation boundary conditions. We first show on the one-dimensional problem why modifying the energy is a necessity in order to obtain stability estimates. We then study the two-dimensional case and propose a modified energy as well as second order extrapolation boundary and corner conditions in order to maintain second order accuracy and stability of the whole scheme, including near the corner.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-2563" status="VALID">
          <idno type="IdRef">08731228X</idno>
          <idno type="RNSR">199814123P</idno>
          <orgName>Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville</orgName>
          <orgName type="acronym">LMPA</orgName>
          <date type="start">1998-01-01</date>
          <desc>
            <address>
              <addrLine>Maison de la Recherche Blaise Pascal 50 rue F.Buisson B.P. 699 62228 Calais Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www-lmpa.univ-littoral.fr/</ref>
          </desc>
          <listRelation>
            <relation name="EA2597" active="#struct-301404" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-1612769" status="VALID">
          <idno type="IdRef">166783900</idno>
          <idno type="ISNI">0000000403836348</idno>
          <idno type="RNSR">200711888W</idno>
          <idno type="ROR">https://ror.org/014vp6c30</idno>
          <orgName>Institut de Mathématiques de Toulouse UMR5219</orgName>
          <orgName type="acronym">IMT</orgName>
          <date type="start">2025-01-01</date>
          <desc>
            <address>
              <addrLine>UT IMT, F-31062 Toulouse Cedex 9, INSA Toulouse, F-31077 Toulouse,France TSE, F-31080 Toulouse, France UT2, F-31058 Toulouse,Téléphone : 05.61.55.67.90</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.math.univ-toulouse.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-116255" type="direct"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation active="#struct-116256" type="direct"/>
            <relation active="#struct-363802" type="direct"/>
            <relation name="UMR5219" active="#struct-441569" type="direct"/>
            <relation active="#struct-1002422" type="direct"/>
            <relation active="#struct-81148" type="indirect"/>
            <relation name="443875" active="#struct-443875" type="indirect"/>
            <relation active="#struct-99539" type="indirect"/>
            <relation name="UMR5314" active="#struct-441569" type="direct"/>
            <relation name="UMR1415" active="#struct-577435" type="indirect"/>
            <relation active="#struct-1574795" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-301404" status="VALID">
          <idno type="IdRef">030969379</idno>
          <idno type="ISNI">0000000121134241</idno>
          <idno type="ROR">https://ror.org/02gdcg342</idno>
          <orgName>Université du Littoral Côte d'Opale</orgName>
          <orgName type="acronym">ULCO</orgName>
          <date type="start">1991-11-07</date>
          <desc>
            <address>
              <addrLine>1, place de l'Yser - BP 7102259375 Dunkerque Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-littoral.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-116255" status="VALID">
          <idno type="IdRef">026388766</idno>
          <idno type="ISNI">0000 0001 2286 8343</idno>
          <idno type="ROR">https://ror.org/01h8pf755</idno>
          <idno type="Wikidata">Q858979</idno>
          <orgName>Institut National des Sciences Appliquées - Toulouse</orgName>
          <orgName type="acronym">INSA Toulouse</orgName>
          <date type="start">1963-10-21</date>
          <desc>
            <address>
              <addrLine>135, avenue de Rangueil - 31077 Toulouse cedex 4</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.insa-toulouse.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301232" type="direct"/>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-301232" status="VALID">
          <idno type="IdRef">162105150</idno>
          <orgName>Institut National des Sciences Appliquées</orgName>
          <orgName type="acronym">INSA</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-443875" status="VALID">
          <idno type="ROR">https://ror.org/017tgbk05</idno>
          <orgName>Communauté d'universités et établissements de Toulouse</orgName>
          <orgName type="acronym">Comue de Toulouse</orgName>
          <desc>
            <address>
              <addrLine>41 Allée Jules Guesde, 31000 Toulouse</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-toulouse.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-116256" status="VALID">
          <idno type="IdRef">026403994</idno>
          <idno type="ROR">https://ror.org/04ezk3x31</idno>
          <orgName>Université Toulouse - Jean Jaurès</orgName>
          <orgName type="acronym">UT2J</orgName>
          <date type="start">1971-01-01</date>
          <desc>
            <address>
              <addrLine>5 allées Antonio Machado - 31058 Toulouse Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-tlse2.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-363802" status="VALID">
          <idno type="IdRef">193857561</idno>
          <orgName>Institut national universitaire Champollion</orgName>
          <orgName type="acronym">INUC</orgName>
          <date type="start">2015-12-01</date>
          <desc>
            <address>
              <addrLine>Place de Verdun - 81012 Albi cedex 09</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-jfc.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </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-1002422" status="VALID">
          <idno type="IdRef">20023269X</idno>
          <idno type="RNSR">201621876N</idno>
          <idno type="ROR">https://ror.org/00ff5f522</idno>
          <orgName>Toulouse School of Economics</orgName>
          <orgName type="acronym">TSE-R</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>1, Esplanade de l'Université, 31080 Toulouse Cedex 06</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.tse-fr.eu</ref>
          </desc>
          <listRelation>
            <relation active="#struct-81148" type="direct"/>
            <relation name="443875" active="#struct-443875" type="indirect"/>
            <relation active="#struct-99539" type="direct"/>
            <relation name="UMR5314" active="#struct-441569" type="direct"/>
            <relation name="UMR1415" active="#struct-577435" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-81148" status="VALID">
          <idno type="IdRef">026404354</idno>
          <idno type="ISNI">0000000121902837</idno>
          <idno type="ROR">https://ror.org/0443n9e75</idno>
          <orgName>Université Toulouse Capitole</orgName>
          <orgName type="acronym">UT Capitole</orgName>
          <date type="start">1970-01-01</date>
          <desc>
            <address>
              <addrLine>2 rue du Doyen-Gabriel-Marty - 31042 Toulouse Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ut-capitole.fr/</ref>
          </desc>
          <listRelation>
            <relation name="443875" active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-99539" status="VALID">
          <idno type="IdRef">026374889</idno>
          <idno type="ROR">https://ror.org/02d9dg697</idno>
          <orgName>École des hautes études en sciences sociales</orgName>
          <orgName type="acronym">EHESS</orgName>
          <date type="start">1975-01-01</date>
          <desc>
            <address>
              <addrLine>54, boulevard Raspail 75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ehess.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-577435" status="VALID">
          <idno type="ROR">https://ror.org/003vg9w96</idno>
          <orgName>Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement</orgName>
          <orgName type="acronym">INRAE</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-1574795" status="VALID">
          <orgName>Université de Toulouse</orgName>
          <orgName type="acronym">EPE UT</orgName>
          <date type="start">2025-01-01</date>
          <desc>
            <address>
              <addrLine>118 toute de Narbonne, 31062 Toulouse cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-tlse3.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-171158" status="VALID">
          <idno type="anr">ANR-24-CE40-3260</idno>
          <orgName>HEAD</orgName>
          <desc>Évolutions hyperboliques, asymptotiques et dynamique</desc>
          <date type="start">2024</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>