<?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-04252310v3</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="2026-05-25T08:44:03+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">$hp$-optimal convergence of the original DG method for linear hyperbolic problems on special simplicial meshes</title>
            <author role="aut">
              <persName>
                <forename type="first">Zhaonan</forename>
                <surname>Dong</surname>
              </persName>
              <email type="md5">0c7635c3b563699c9d8d4072f43545c5</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">zhaonan-dong</idno>
              <idno type="idhal" notation="numeric">1570558</idno>
              <idno type="halauthorid" notation="string">2127601-1570558</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-4083-6593</idno>
              <affiliation ref="#struct-454687"/>
              <affiliation ref="#struct-51621"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Lorenzo</forename>
                <surname>Mascotto</surname>
              </persName>
              <idno type="halauthorid">2127602-0</idno>
              <affiliation ref="#struct-60273"/>
              <affiliation ref="#struct-73335"/>
              <affiliation ref="#struct-300742"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Zhaonan</forename>
                <surname>Dong</surname>
              </persName>
              <email type="md5">0c7635c3b563699c9d8d4072f43545c5</email>
              <email type="domain">inria.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2023-10-20 17:10:47</date>
            </edition>
            <edition n="v2">
              <date type="whenSubmitted">2023-11-08 17:31:20</date>
            </edition>
            <edition n="v3" type="current">
              <date type="whenSubmitted">2024-07-09 01:44:38</date>
              <date type="whenModified">2026-03-26 03:03:14</date>
              <date type="whenReleased">2024-07-09 09:21:32</date>
              <date type="whenProduced">2024-08-31</date>
              <date type="whenEndEmbargoed">2024-07-09</date>
              <ref type="file" target="https://inria.hal.science/hal-04252310v3/document">
                <date notBefore="2024-07-09"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://inria.hal.science/hal-04252310v3/file/main.pdf" id="file-4639354-4027870">
                <date notBefore="2024-07-09"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="938972">
                <persName>
                  <forename>Zhaonan</forename>
                  <surname>Dong</surname>
                </persName>
                <email type="md5">0c7635c3b563699c9d8d4072f43545c5</email>
                <email type="domain">inria.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-04252310</idno>
            <idno type="halUri">https://inria.hal.science/hal-04252310</idno>
            <idno type="halBibtex">dong:hal-04252310</idno>
            <idno type="halRefHtml">&lt;i&gt;IMA Journal of Numerical Analysis&lt;/i&gt;, inPress, &lt;a target="_blank" href="https://dx.doi.org/10.1093/imanum/drae051"&gt;&amp;#x27E8;10.1093/imanum/drae051&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">IMA Journal of Numerical Analysis, inPress, &amp;#x27E8;10.1093/imanum/drae051&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://creativecommons.org/licenses/by/4.0/">CC BY 4.0 - Attribution<ref corresp="#file-4639354-4027870"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="ENPC" corresp="PARISTECH">École nationale des ponts et chaussées </idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="INRIA-ROCQ">INRIA Paris - Rocquencourt</idno>
            <idno type="stamp" n="CERMICS" corresp="ENPC">Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</idno>
            <idno type="stamp" n="IP_PARIS">Institut Polytechnique de Paris</idno>
            <idno type="stamp" n="IP-PARIS-DEPARTEMENT-MATHEMATIQUES">Département de Mathèmatiques</idno>
            <idno type="stamp" n="IP-PARIS-MATHEMATIQUES">IP Paris Département de Mathématiques</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">$hp$-optimal convergence of the original DG method for linear hyperbolic problems on special simplicial meshes</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Zhaonan</forename>
                    <surname>Dong</surname>
                  </persName>
                  <email type="md5">0c7635c3b563699c9d8d4072f43545c5</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">zhaonan-dong</idno>
                  <idno type="idhal" notation="numeric">1570558</idno>
                  <idno type="halauthorid" notation="string">2127601-1570558</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-4083-6593</idno>
                  <affiliation ref="#struct-454687"/>
                  <affiliation ref="#struct-51621"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Lorenzo</forename>
                    <surname>Mascotto</surname>
                  </persName>
                  <idno type="halauthorid">2127602-0</idno>
                  <affiliation ref="#struct-60273"/>
                  <affiliation ref="#struct-73335"/>
                  <affiliation ref="#struct-300742"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">14102</idno>
                <idno type="issn">0272-4979</idno>
                <idno type="eissn">1464-3642</idno>
                <title level="j">IMA Journal of Numerical Analysis</title>
                <imprint>
                  <publisher>Oxford University Press (OUP)</publisher>
                  <date type="datePub" subtype="inPress">2024-08-31</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1093/imanum/drae051</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Discontinuous Galerkin</term>
                <term xml:lang="en">Optimal convergence</term>
                <term xml:lang="en">Linear hyperbolic problems</term>
                <term xml:lang="en">A priori error estimation</term>
                <term xml:lang="en">p-version.</term>
              </keywords>
              <classCode scheme="classification">AMS subject classification: 65N12; 65N30; 65N50</classCode>
              <classCode scheme="halDomain" n="math">Mathematics [math]</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 prove hp-optimal error estimates for the original DG method when approximating solutions to first-order hyperbolic problems with constant convection fields in the $L^2$ and DG norms. The main theoretical tools used in the analysis are novel $hp$-optimal approximation properties of the special projector introduced in [Cockburn, Dong, Guzman, SINUM, 2008]. We assess the numerical results on some test cases.</p>
            </abstract>
            <particDesc>
              <org type="consortium">Serena</org>
            </particDesc>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-454687" status="VALID">
          <idno type="RNSR">201521772E</idno>
          <idno type="ROR">https://ror.org/00e5h1370</idno>
          <orgName>Simulation for the Environment: Reliable and Efficient Numerical Algorithms</orgName>
          <orgName type="acronym">SERENA</orgName>
          <date type="start">2015-12-31</date>
          <date type="end">2027-12-31</date>
          <desc>
            <address>
              <addrLine>48 Rue Barrault, 75013 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/serena</ref>
          </desc>
          <listRelation>
            <relation active="#struct-454310" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation active="#struct-1771827" type="direct"/>
            <relation name="UMR9032" active="#struct-441569" type="indirect"/>
            <relation active="#struct-1226401" type="indirect"/>
            <relation active="#struct-563936" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-51621" status="OLD">
          <idno type="IdRef">151174822</idno>
          <idno type="ISNI">0000000403826254</idno>
          <idno type="RNSR">200320607R</idno>
          <idno type="ROR">https://ror.org/03wct8w46</idno>
          <idno type="Wikidata">Q51781803</idno>
          <orgName>Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique</orgName>
          <orgName type="acronym">CERMICS</orgName>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>6 et 8 avenue Blaise Pascal Cité Descartes - Champs sur Marne 77455 Marne la Vallée Cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://cermics.enpc.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301545" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-60273" status="VALID">
          <idno type="IdRef">097494496</idno>
          <idno type="ROR">https://ror.org/01ynf4891</idno>
          <orgName>Università degli Studi di Milano-Bicocca = University of Milano-Bicocca</orgName>
          <orgName type="acronym">UNIMIB</orgName>
          <date type="start">1998-06-10</date>
          <desc>
            <address>
              <addrLine>Piazza dell'Ateneo Nuovo, 1 - 20126, Milano</addrLine>
              <country key="IT"/>
            </address>
            <ref type="url">https://www.unimib.it/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-73335" status="VALID">
          <orgName>Istituto di Matematica Applicata e Tecnologie Informatiche</orgName>
          <orgName type="acronym">IMATI-CNR</orgName>
          <desc>
            <address>
              <addrLine>Via Ferrata, 1, 27100 Pavia - Italy</addrLine>
              <country key="IT"/>
            </address>
            <ref type="url">http://www.imati.cnr.it/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-254021" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-300742" status="VALID">
          <idno type="ISNI">0000 0001 2286 1424</idno>
          <idno type="ROR">https://ror.org/03prydq77</idno>
          <orgName>Universität Wien = University of Vienna</orgName>
          <date type="start">1365-01-01</date>
          <desc>
            <address>
              <addrLine>Universitätsring 1, 1010 Wien</addrLine>
              <country key="AT"/>
            </address>
            <ref type="url">https://www.univie.ac.at/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-454310" status="VALID">
          <idno type="IdRef">241614864</idno>
          <idno type="RNSR">196718247G</idno>
          <idno type="ROR">https://ror.org/05eyd5d35</idno>
          <orgName>Centre Inria de Paris</orgName>
          <date type="start">2016-03-10</date>
          <desc>
            <address>
              <addrLine>48 Rue Barrault, 75013 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/paris</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300009" status="VALID">
          <idno type="ROR">https://ror.org/02kvxyf05</idno>
          <orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
          <orgName type="acronym">Inria</orgName>
          <desc>
            <address>
              <addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/en/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-1771827" status="VALID">
          <idno type="IdRef">151174822</idno>
          <idno type="ISNI">0000000403826254</idno>
          <idno type="RNSR">200320607R</idno>
          <idno type="ROR">https://ror.org/03wct8w46</idno>
          <idno type="Wikidata">Q51781803</idno>
          <orgName>Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique</orgName>
          <orgName type="acronym">CERMICS UMR 9032</orgName>
          <date type="start">2026-01-01</date>
          <desc>
            <address>
              <addrLine>6 et 8 avenue Blaise Pascal Cité Descartes - Champs sur Marne 77455 Marne la Vallée Cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://cermics.enpc.fr/</ref>
          </desc>
          <listRelation>
            <relation name="UMR9032" active="#struct-441569" type="direct"/>
            <relation active="#struct-1226401" type="direct"/>
            <relation active="#struct-563936" type="indirect"/>
          </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="institution" xml:id="struct-1226401" status="VALID">
          <idno type="IdRef">026375060</idno>
          <idno type="ISNI">0000000406414845</idno>
          <idno type="ROR">https://ror.org/02nwvxz07</idno>
          <idno type="Wikidata">Q273523</idno>
          <orgName>École nationale des ponts et chaussées</orgName>
          <orgName type="acronym">ENPC</orgName>
          <date type="start">2024-07-17</date>
          <desc>
            <address>
              <addrLine>6-8 avenue Blaise PascalCité DescartesChamps-sur-Marne77455 Marne-la-Vallée cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://ecoledesponts.fr/</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-254021" status="VALID">
          <idno type="ISNI">0000 0001 2159 6200</idno>
          <idno type="ROR">https://ror.org/04zaypm56</idno>
          <orgName>National Research Council of Italy | Consiglio Nazionale delle Ricerche</orgName>
          <orgName type="acronym">CNR</orgName>
          <date type="start">1923-01-01</date>
          <desc>
            <address>
              <addrLine>Piazzale Aldo Moro, 7 - 00185 Roma</addrLine>
              <country key="IT"/>
            </address>
            <ref type="url">https://www.cnr.it/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>