<?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-01114666v2</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="2026-05-25T09:33:20+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Stability of finite difference schemes for hyperbolic initial boundary value problems: numerical boundary layers</title>
            <author role="crp">
              <persName>
                <forename type="first">Benjamin</forename>
                <surname>Boutin</surname>
              </persName>
              <email type="md5">24b215516064ee227734108155dd2393</email>
              <email type="domain">univ-rennes.fr</email>
              <ptr type="url" target="https://perso.univ-rennes1.fr/benjamin.boutin/"/>
              <idno type="idhal" notation="string">benjamin-boutin</idno>
              <idno type="idhal" notation="numeric">2434</idno>
              <idno type="halauthorid" notation="string">15126-2434</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-4012-6922</idno>
              <idno type="IDREF">https://www.idref.fr/143317881</idno>
              <idno type="ARXIV">https://arxiv.org/a/boutin_b_1</idno>
              <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=Juuwg8MAAAAJ</idno>
              <affiliation ref="#struct-75"/>
            </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-394163"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Benjamin</forename>
                <surname>Boutin</surname>
              </persName>
              <email type="md5">24b215516064ee227734108155dd2393</email>
              <email type="domain">univ-rennes.fr</email>
            </editor>
            <funder ref="#projanr-36344"/>
            <funder ref="#projanr-41179"/>
            <funder ref="#projanr-38048"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2015-02-09 17:02:21</date>
            </edition>
            <edition n="v2" type="current">
              <date type="whenSubmitted">2023-06-16 13:57:00</date>
              <date type="whenWritten">2015-02-09</date>
              <date type="whenModified">2025-04-04 18:27:35</date>
              <date type="whenReleased">2023-06-16 14:02:47</date>
              <date type="whenProduced">2017-06-20</date>
              <date type="whenEndEmbargoed">2023-06-16</date>
              <ref type="file" target="https://hal.science/hal-01114666v2/document">
                <date notBefore="2023-06-16"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-01114666v2/file/Boutin-Coulombel.pdf" id="file-4131076-3596491">
                <date notBefore="2023-06-16"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/1502.02634"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="142129">
                <persName>
                  <forename>Benjamin</forename>
                  <surname>Boutin</surname>
                </persName>
                <email type="md5">24b215516064ee227734108155dd2393</email>
                <email type="domain">univ-rennes.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01114666</idno>
            <idno type="halUri">https://hal.science/hal-01114666</idno>
            <idno type="halBibtex">boutin:hal-01114666</idno>
            <idno type="halRefHtml">&lt;i&gt;Numerical Mathematics: Theory, Methods and Applications&lt;/i&gt;, 2017, 10 (3), pp.489-519. &lt;a target="_blank" href="https://dx.doi.org/10.4208/nmtma.2017.m1525"&gt;&amp;#x27E8;10.4208/nmtma.2017.m1525&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Numerical Mathematics: Theory, Methods and Applications, 2017, 10 (3), pp.489-519. &amp;#x27E8;10.4208/nmtma.2017.m1525&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-4131076-3596491"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-NANTES">Université de Nantes</idno>
            <idno type="stamp" n="UNIV-RENNES1">Université de Rennes 1</idno>
            <idno type="stamp" n="IRMAR">Institut de Recherche Mathématique de Rennes</idno>
            <idno type="stamp" n="LMJL">Laboratoire de Mathématiques Jean Leray</idno>
            <idno type="stamp" n="UR2-HB">Université Rennes 2 - Haute Bretagne</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INSA-RENNES">Institut National des Sciences Appliquées de Rennes</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="UNAM">l'unam - université nantes angers le mans</idno>
            <idno type="stamp" n="IRMAR-AN">Analyse numérique</idno>
            <idno type="stamp" n="IRMAR-EDP" corresp="IRMAR">Equations aux dérivées partielles</idno>
            <idno type="stamp" n="CHL">Centre Henri Lebesgue</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="UR1-HAL">Publications labos UR1 dans HAL-Rennes 1</idno>
            <idno type="stamp" n="UR1-MATH-STIC">UR1 - publications Maths-STIC</idno>
            <idno type="stamp" n="AGREENIUM">Archive ouverte en agrobiosciences</idno>
            <idno type="stamp" n="UNIV-RENNES2">Université Rennes 2</idno>
            <idno type="stamp" n="TEST-UR-CSS">TEST Université de Rennes CSS</idno>
            <idno type="stamp" n="UNIV-RENNES">Université de Rennes</idno>
            <idno type="stamp" n="INSA-GROUPE">Groupe INSA</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="UR1-MATH-NUM">Pôle UnivRennes - Mathématiques - Numérique </idno>
            <idno type="stamp" n="NANTES-UNIVERSITE">Nantes Université</idno>
            <idno type="stamp" n="UNIV-NANTES-AV2022">Université de Nantes</idno>
            <idno type="stamp" n="INSTITUT-AGRO">Institut Agro</idno>
            <idno type="stamp" n="IRMAR-ANM">Equipe Analyse numérique et modélisation - IRMAR</idno>
            <idno type="stamp" n="IRMAR-ANUM" corresp="IRMAR">Equipe Analyse numérique et modélisation - IRMAR</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">Stability of finite difference schemes for hyperbolic initial boundary value problems: numerical boundary layers</title>
                <author role="crp">
                  <persName>
                    <forename type="first">Benjamin</forename>
                    <surname>Boutin</surname>
                  </persName>
                  <email type="md5">24b215516064ee227734108155dd2393</email>
                  <email type="domain">univ-rennes.fr</email>
                  <ptr type="url" target="https://perso.univ-rennes1.fr/benjamin.boutin/"/>
                  <idno type="idhal" notation="string">benjamin-boutin</idno>
                  <idno type="idhal" notation="numeric">2434</idno>
                  <idno type="halauthorid" notation="string">15126-2434</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-4012-6922</idno>
                  <idno type="IDREF">https://www.idref.fr/143317881</idno>
                  <idno type="ARXIV">https://arxiv.org/a/boutin_b_1</idno>
                  <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=Juuwg8MAAAAJ</idno>
                  <affiliation ref="#struct-75"/>
                </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-394163"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">40080</idno>
                <idno type="issn">1004-8979</idno>
                <idno type="eissn">2079-7338</idno>
                <title level="j">Numerical Mathematics: Theory, Methods and Applications</title>
                <imprint>
                  <publisher>GSP / Nanjing University Press</publisher>
                  <biblScope unit="volume">10</biblScope>
                  <biblScope unit="issue">3</biblScope>
                  <biblScope unit="pp">489-519</biblScope>
                  <date type="datePub">2017-06-20</date>
                  <date type="dateEpub">2017-06-20</date>
                </imprint>
              </monogr>
              <idno type="arxiv">1502.02634</idno>
              <idno type="doi">10.4208/nmtma.2017.m1525</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">numerical schemes</term>
                <term xml:lang="en">stability</term>
                <term xml:lang="en">boundary layers</term>
                <term xml:lang="en">Dirichlet boundary condition</term>
              </keywords>
              <classCode scheme="classification">65M12, 65M06, 65M20</classCode>
              <classCode scheme="halDomain" n="math.math-ap">Mathematics [math]/Analysis of PDEs [math.AP]</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>In this article, we give a unified theory for constructing boundary layer expansions for discretized transport equations with homogeneous Dirichlet boundary conditions. We exhibit a natural assumption on the discretization under which the numerical solution can be written approximately as a two-scale boundary layer expansion. In particular, this expansion yields discrete semigroup estimates that are compatible with the continuous semigroup estimates in the limit where the space and time steps tend to zero. The novelty of our approach is to cover numerical schemes with arbitrarily many time levels, while semigroup estimates were restricted, up to now, to numerical schemes with two time levels only.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-75" status="OLD">
          <idno type="IdRef">028233107</idno>
          <idno type="RNSR">199612396W</idno>
          <idno type="ROR">https://ror.org/05y76vp22</idno>
          <orgName>Institut de Recherche Mathématique de Rennes</orgName>
          <orgName type="acronym">IRMAR</orgName>
          <date type="start">1996-01-01</date>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <addrLine>Campus de Beaulieu, bâtiments 22 et 23, 263 avenue du Général Leclerc, CS 7420535042  RENNES Cédex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://irmar.univ-rennes1.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-105160" type="direct"/>
            <relation active="#struct-117606" type="direct"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-247362" type="direct"/>
            <relation active="#struct-406201" type="direct"/>
            <relation name="UMR6625" active="#struct-441569" type="direct"/>
            <relation active="#struct-1090536" type="direct"/>
            <relation active="#struct-1042499" type="indirect"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-394163" status="OLD">
          <orgName>Equations aux dérivées partielles</orgName>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-37" type="direct"/>
            <relation active="#struct-97058" type="indirect"/>
            <relation active="#struct-93263" type="indirect"/>
            <relation name="UMR6629" active="#struct-441569" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-105160" status="VALID">
          <idno type="IdRef">26693823X</idno>
          <idno type="ROR">https://ror.org/015m7wh34</idno>
          <orgName>Université de Rennes</orgName>
          <orgName type="acronym">UR</orgName>
          <desc>
            <address>
              <addrLine>Campus de Beaulieu, 263 avenue Général Leclerc, CS 74205, 35042 RENNES CEDEX</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-rennes.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-117606" status="VALID">
          <idno type="ROR">https://ror.org/04xaa4j22</idno>
          <orgName>Institut National des Sciences Appliquées - Rennes</orgName>
          <orgName type="acronym">INSA Rennes</orgName>
          <desc>
            <address>
              <addrLine>20, avenue des Buttes de Coësmes - CS 70839 - 35708 Rennes cedex 7</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.insa-rennes.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301232" 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="institution" xml:id="struct-247362" status="VALID">
          <idno type="ROR">https://ror.org/03rxtdc22</idno>
          <orgName>École normale supérieure - Rennes</orgName>
          <orgName type="acronym">ENS Rennes</orgName>
          <desc>
            <address>
              <addrLine>Campus de Ker Lann - avenue Robert Schuman - 35170 Bruz</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ens-rennes.fr</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-406201" status="VALID">
          <idno type="IdRef">054447658</idno>
          <idno type="ISNI">0000000121522279</idno>
          <idno type="ROR">https://ror.org/01m84wm78</idno>
          <orgName>Université de Rennes 2</orgName>
          <orgName type="acronym">UR2</orgName>
          <desc>
            <address>
              <addrLine>Place du recteur Henri Le Moal - CS 24307 - 35043 Rennes cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-rennes2.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="institution" xml:id="struct-1090536" status="OLD">
          <idno type="ROR">https://ror.org/01s3fs709</idno>
          <orgName>INSTITUT AGRO Agrocampus Ouest</orgName>
          <date type="start">2020-01-01</date>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <addrLine>65 rue de Saint Brieuc CS 84215 35042 Rennes CEDEX</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-1042499" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-1042499" status="VALID">
          <idno type="IdRef">260373249</idno>
          <idno type="ROR">https://ror.org/01dkyve95</idno>
          <orgName>Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement</orgName>
          <orgName type="acronym">Institut Agro</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.institut-agro.fr</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-37" status="OLD">
          <idno type="IdRef">087220865</idno>
          <idno type="ISNI">0000000097740814</idno>
          <idno type="RNSR">199612400A</idno>
          <orgName>Laboratoire de Mathématiques Jean Leray</orgName>
          <orgName type="acronym">LMJL</orgName>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.math.sciences.univ-nantes.fr/jeanleray/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-97058" type="direct"/>
            <relation active="#struct-93263" type="indirect"/>
            <relation name="UMR6629" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="regrouplaboratory" xml:id="struct-97058" status="OLD">
          <orgName>Université de Nantes - UFR des Sciences et des Techniques</orgName>
          <orgName type="acronym">UN UFR ST</orgName>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <addrLine>2, rue de la Houssinière - BP 92208 - 44322 Nantes cedex 3</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.sciences-techniques.univ-nantes.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-93263" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-93263" status="OLD">
          <idno type="IdRef">026403447</idno>
          <idno type="ROR">https://ror.org/03gnr7b55</idno>
          <orgName>Université de Nantes</orgName>
          <orgName type="acronym">UN</orgName>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <addrLine>1, quai de Tourville - BP 13522 - 44035 Nantes cedex 1</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-nantes.fr/</ref>
          </desc>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-36344" status="VALID">
          <idno type="anr">ANR-13-BS01-0009</idno>
          <idno type="program">Blanc 2013</idno>
          <orgName>BoND</orgName>
          <desc>Frontières, numérique, dispersion.</desc>
          <date type="start">2013</date>
        </org>
        <org type="anrProject" xml:id="projanr-41179" status="VALID">
          <idno type="anr">ANR-14-CE25-0001</idno>
          <idno type="program">Appel à projets générique</idno>
          <orgName>ACHYLLES</orgName>
          <desc>Capture de l'Asymptotique pour des Systèmes Hyperboliques de Lois de Conservation avec Termes Source</desc>
          <date type="start">2014</date>
        </org>
        <org type="anrProject" xml:id="projanr-38048" status="VALID">
          <idno type="anr">ANR-11-LABX-0020</idno>
          <idno type="program">Laboratoires d'excellence</idno>
          <orgName>LEBESGUE</orgName>
          <desc>Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation</desc>
          <date type="start">2011</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>