<?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 cea-04211874v1</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="2026-05-26T06:26:27+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Arbitrary order monotonic finite-volume schemes for 2D elliptic problems</title>
            <author role="aut">
              <persName>
                <forename type="first">Xavier</forename>
                <surname>Blanc</surname>
              </persName>
              <email type="md5">987a84acac80faf94a7aaf41f739ad66</email>
              <email type="domain">u-paris.fr</email>
              <idno type="idhal" notation="string">blanc</idno>
              <idno type="idhal" notation="numeric">3244</idno>
              <idno type="halauthorid" notation="string">23434-3244</idno>
              <idno type="IDREF">https://www.idref.fr/188473718</idno>
              <idno type="RESEARCHERID">http://www.researcherid.com/rid/3244</idno>
              <idno type="RESEARCHERID">http://www.researcherid.com/rid/1116291</idno>
              <idno type="RESEARCHERID">http://www.researcherid.com/rid/11177</idno>
              <affiliation ref="#struct-1005052"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Francois</forename>
                <surname>Hermeline</surname>
              </persName>
              <email type="md5">90772653b8daa8514909c9bf3e56370f</email>
              <email type="domain">cea.fr</email>
              <idno type="idhal" notation="numeric">1116292</idno>
              <idno type="halauthorid" notation="string">2332867-1116292</idno>
              <affiliation ref="#struct-429838"/>
              <affiliation ref="#struct-1055205"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Emmanuel</forename>
                <surname>Labourasse</surname>
              </persName>
              <email type="md5">6f3c931382935bb13be348689d31d3df</email>
              <email type="domain">gmail.com</email>
              <idno type="idhal" notation="string">emmanuellabourasse</idno>
              <idno type="idhal" notation="numeric">1105925</idno>
              <idno type="halauthorid" notation="string">24406-1105925</idno>
              <affiliation ref="#struct-429838"/>
              <affiliation ref="#struct-1055205"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Julie</forename>
                <surname>Patela</surname>
              </persName>
              <email type="md5">9cfb6141c07f940398a6e1494ffec833</email>
              <email type="domain">hotmail.fr</email>
              <idno type="idhal" notation="numeric">1116290</idno>
              <idno type="halauthorid" notation="string">2332866-1116290</idno>
              <affiliation ref="#struct-1005052"/>
              <affiliation ref="#struct-429838"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Julie</forename>
                <surname>PATELA</surname>
              </persName>
              <email type="md5">9cfb6141c07f940398a6e1494ffec833</email>
              <email type="domain">hotmail.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2023-09-20 09:00:47</date>
              <date type="whenModified">2025-03-20 09:24:02</date>
              <date type="whenReleased">2023-09-20 10:08:21</date>
              <date type="whenProduced">2023-09-20</date>
              <date type="whenEndEmbargoed">2023-09-20</date>
              <ref type="file" target="https://cea.hal.science/cea-04211874v1/document">
                <date notBefore="2023-09-20"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://cea.hal.science/cea-04211874v1/file/article_2D_High_Order.pdf" id="file-4211874-3673282">
                <date notBefore="2023-09-20"/>
              </ref>
            </edition>
            <edition n="v2">
              <date type="whenSubmitted">2024-08-06 09:46:12</date>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="1096187">
                <persName>
                  <forename>Julie</forename>
                  <surname>PATELA</surname>
                </persName>
                <email type="md5">9cfb6141c07f940398a6e1494ffec833</email>
                <email type="domain">hotmail.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">cea-04211874</idno>
            <idno type="halUri">https://cea.hal.science/cea-04211874</idno>
            <idno type="halBibtex">blanc:cea-04211874</idno>
            <idno type="halRefHtml">2023</idno>
            <idno type="halRef">2023</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-4211874-3673282"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt/>
          <notesStmt/>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Arbitrary order monotonic finite-volume schemes for 2D elliptic problems</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Xavier</forename>
                    <surname>Blanc</surname>
                  </persName>
                  <email type="md5">987a84acac80faf94a7aaf41f739ad66</email>
                  <email type="domain">u-paris.fr</email>
                  <idno type="idhal" notation="string">blanc</idno>
                  <idno type="idhal" notation="numeric">3244</idno>
                  <idno type="halauthorid" notation="string">23434-3244</idno>
                  <idno type="IDREF">https://www.idref.fr/188473718</idno>
                  <idno type="RESEARCHERID">http://www.researcherid.com/rid/3244</idno>
                  <idno type="RESEARCHERID">http://www.researcherid.com/rid/1116291</idno>
                  <idno type="RESEARCHERID">http://www.researcherid.com/rid/11177</idno>
                  <affiliation ref="#struct-1005052"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Francois</forename>
                    <surname>Hermeline</surname>
                  </persName>
                  <email type="md5">90772653b8daa8514909c9bf3e56370f</email>
                  <email type="domain">cea.fr</email>
                  <idno type="idhal" notation="numeric">1116292</idno>
                  <idno type="halauthorid" notation="string">2332867-1116292</idno>
                  <affiliation ref="#struct-429838"/>
                  <affiliation ref="#struct-1055205"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Emmanuel</forename>
                    <surname>Labourasse</surname>
                  </persName>
                  <email type="md5">6f3c931382935bb13be348689d31d3df</email>
                  <email type="domain">gmail.com</email>
                  <idno type="idhal" notation="string">emmanuellabourasse</idno>
                  <idno type="idhal" notation="numeric">1105925</idno>
                  <idno type="halauthorid" notation="string">24406-1105925</idno>
                  <affiliation ref="#struct-429838"/>
                  <affiliation ref="#struct-1055205"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Julie</forename>
                    <surname>Patela</surname>
                  </persName>
                  <email type="md5">9cfb6141c07f940398a6e1494ffec833</email>
                  <email type="domain">hotmail.fr</email>
                  <idno type="idhal" notation="numeric">1116290</idno>
                  <idno type="halauthorid" notation="string">2332866-1116290</idno>
                  <affiliation ref="#struct-1005052"/>
                  <affiliation ref="#struct-429838"/>
                </author>
              </analytic>
              <monogr>
                <imprint>
                  <date type="datePub">2023-09-20</date>
                </imprint>
              </monogr>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Finite volume method elliptic problem anisotropic diffusion monotonicity high order</term>
                <term xml:lang="en">Finite volume method</term>
                <term xml:lang="en">elliptic problem</term>
                <term xml:lang="en">anisotropic diffusion</term>
                <term xml:lang="en">monotonicity</term>
                <term xml:lang="en">high order</term>
              </keywords>
              <classCode scheme="halDomain" n="math.math-ap">Mathematics [math]/Analysis of PDEs [math.AP]</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>Monotonicity is very important in most applications solving elliptic problems. Many schemes preserving positivity has been proposed but are at most second-order convergent. Besides, in general, high-order schemes do not preserve positivity. In the present paper, we propose an arbitrary-order monotonic method for elliptic problems in 2D. We show how to adapt our method to the case of a discontinuous and/or tensorvalued diffusion coefficient, while keeping the order of convergence. We assess the new scheme on several test problems.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-1005052" status="VALID">
          <idno type="IdRef">099222221</idno>
          <idno type="ISNI">0000000101748385</idno>
          <idno type="RNSR">199712644L</idno>
          <idno type="ROR">https://ror.org/04xmteb38</idno>
          <orgName>Laboratoire Jacques-Louis Lions</orgName>
          <orgName type="acronym">LJLL (UMR_7598)</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>Sorbonne-Université, Boîte courrier 187 - 75252 Paris Cedex 05</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ljll.math.upmc.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-413221" type="direct"/>
            <relation name="UMR7598" active="#struct-441569" type="direct"/>
            <relation name="UMR_7598" active="#struct-557826" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-429838" status="VALID">
          <orgName>CEA/DAM [Arpajon]</orgName>
          <orgName type="acronym">CEA/DAM</orgName>
          <desc>
            <address>
              <addrLine>2 Rue de la Piquetterie91680 Bruyères-le-Châtel</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-5981" type="direct"/>
            <relation name="DAM" active="#struct-300016" type="indirect"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-1055205" status="VALID">
          <orgName>Laboratoire en Informatique Haute Performance pour le Calcul et la simulation</orgName>
          <orgName type="acronym">LIHPC</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>CEA Bruyères-le-Châtel 91297 Arpajon cedex</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-119523" type="direct"/>
            <relation name="DAM/DIF" active="#struct-5981" type="indirect"/>
            <relation name="DAM" active="#struct-300016" type="indirect"/>
            <relation active="#struct-419361" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-413221" status="VALID">
          <idno type="IdRef">221333754</idno>
          <idno type="ROR">https://ror.org/02en5vm52</idno>
          <orgName>Sorbonne Université</orgName>
          <orgName type="acronym">SU</orgName>
          <date type="start">2018-01-01</date>
          <desc>
            <address>
              <addrLine>21 rue de l’École de médecine - 75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.sorbonne-universite.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-557826" status="VALID">
          <idno type="IdRef">236453505</idno>
          <idno type="ISNI">0000 0004 7885 7602</idno>
          <idno type="ROR">https://ror.org/05f82e368</idno>
          <orgName>Université Paris Cité</orgName>
          <orgName type="acronym">UPCité</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>85 boulevard Saint-Germain75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://u-paris.fr/</ref>
          </desc>
        </org>
        <org type="regrouplaboratory" xml:id="struct-5981" status="VALID">
          <idno type="IdRef">026372096</idno>
          <idno type="ISNI">0000000119569481</idno>
          <idno type="ROR">https://ror.org/00kn4eb29</idno>
          <idno type="Wikidata">Q2931222</idno>
          <orgName>Direction des Applications Militaires</orgName>
          <orgName type="acronym">DAM</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www-dam.cea.fr/</ref>
          </desc>
          <listRelation>
            <relation name="DAM" active="#struct-300016" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300016" status="VALID">
          <idno type="IdRef">026372061</idno>
          <idno type="ISNI">0000000122998025</idno>
          <idno type="ROR">https://ror.org/00jjx8s55</idno>
          <idno type="Wikidata">Q868550</idno>
          <orgName>Commissariat à l'énergie atomique et aux énergies alternatives</orgName>
          <orgName type="acronym">CEA</orgName>
          <desc>
            <address>
              <addrLine>Centre de SaclayCentre de GrenobleCentre de Cadaracheetc</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.cea.fr/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-119523" status="VALID">
          <orgName>DAM Île-de-France</orgName>
          <orgName type="acronym">DAM/DIF</orgName>
          <desc>
            <address>
              <addrLine>CEA Bruyères-le-Châtel 91297 Arpajon cedex</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation name="DAM/DIF" active="#struct-5981" type="direct"/>
            <relation name="DAM" active="#struct-300016" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-419361" status="VALID">
          <idno type="IdRef">241345251</idno>
          <idno type="ROR">https://ror.org/03xjwb503</idno>
          <orgName>Université Paris-Saclay</orgName>
          <desc>
            <address>
              <addrLine>Bâtiment Bréguet, 3 Rue Joliot Curie 2e ét, 91190 Gif-sur-Yvette</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.universite-paris-saclay.fr/fr</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>