<?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-01313353</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="2026-05-03T23:44:00+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Vertex Approximate Gradient Scheme for Hybrid Dimensional Two-Phase Darcy Flows in Fractured Porous Media </title>
            <author role="aut">
              <persName>
                <forename type="first">Konstantin</forename>
                <surname>Brenner</surname>
              </persName>
              <idno type="halauthorid">509189-0</idno>
              <orgName ref="#struct-168891"/>
              <affiliation ref="#struct-168891"/>
              <affiliation ref="#struct-199970"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Mayya</forename>
                <surname>Groza</surname>
              </persName>
              <email type="md5">9e93eda3848ad8a054c50c72042e190a</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="numeric">981962</idno>
              <idno type="halauthorid" notation="string">782233-981962</idno>
              <orgName ref="#struct-168891"/>
              <affiliation ref="#struct-199970"/>
              <affiliation ref="#struct-168891"/>
            </author>
            <author role="crp">
              <persName>
                <forename type="first">Cindy</forename>
                <surname>Guichard</surname>
              </persName>
              <email type="md5">841cd20eaf370dd8bab865011d9741c4</email>
              <email type="domain">ljll.math.upmc.fr</email>
              <idno type="idhal" notation="string">cindy-guichard-26</idno>
              <idno type="idhal" notation="numeric">1115859</idno>
              <idno type="halauthorid" notation="string">513465-1115859</idno>
              <idno type="IDREF">https://www.idref.fr/158768493</idno>
              <orgName ref="#struct-454317"/>
              <affiliation ref="#struct-454317"/>
              <affiliation ref="#struct-25"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Roland</forename>
                <surname>Masson</surname>
              </persName>
              <email type="md5">ef118128bac0e07bb86886f24e6fdcf4</email>
              <email type="domain">univ-cotedazur.fr</email>
              <idno type="idhal" notation="string">roland-masson</idno>
              <idno type="idhal" notation="numeric">21126</idno>
              <idno type="halauthorid" notation="string">13248-21126</idno>
              <idno type="IDREF">https://www.idref.fr/035818689</idno>
              <idno type="ORCID">https://orcid.org/0009-0006-8713-3069</idno>
              <orgName ref="#struct-168891"/>
              <affiliation ref="#struct-199970"/>
              <affiliation ref="#struct-168891"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Konstantin</forename>
                <surname>Brenner</surname>
              </persName>
              <email type="md5">90a124ce108079f82a5335c3cb839d0a</email>
              <email type="domain">gmail.com</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2016-05-09 20:00:10</date>
              <date type="whenModified">2025-08-26 15:21:01</date>
              <date type="whenReleased">2016-05-10 11:05:38</date>
              <date type="whenProduced">2014-06-15</date>
              <date type="whenEndEmbargoed">2016-05-09</date>
              <ref type="file" target="https://hal.science/hal-01313353v1/document">
                <date notBefore="2016-05-09"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-01313353v1/file/fvca7-VagDFN.pdf" id="file-1313353-1393114">
                <date notBefore="2016-05-09"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="170618">
                <persName>
                  <forename>Konstantin</forename>
                  <surname>Brenner</surname>
                </persName>
                <email type="md5">90a124ce108079f82a5335c3cb839d0a</email>
                <email type="domain">gmail.com</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01313353</idno>
            <idno type="halUri">https://hal.science/hal-01313353</idno>
            <idno type="halBibtex">brenner:hal-01313353</idno>
            <idno type="halRefHtml">&lt;i&gt;The International Symposium of Finite Volumes for Complex Applications VII&lt;/i&gt;, Jun 2014, Berlin, Germany</idno>
            <idno type="halRef">The International Symposium of Finite Volumes for Complex Applications VII, Jun 2014, Berlin, Germany</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-1313353-1393114"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNICE">Université Nice Sophia Antipolis</idno>
            <idno type="stamp" n="UNIV-PARIS7" corresp="UNIV-PARIS">Université Denis Diderot - Paris VII</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="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="INRIA-SOPHIA">INRIA Sophia Antipolis - Méditerranée</idno>
            <idno type="stamp" n="INRIA-ROCQ">INRIA Paris - Rocquencourt</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="INRIASO">INRIA-SOPHIA</idno>
            <idno type="stamp" n="DIEUDONNE">Laboratoire Jean-Alexandre Dieudonné</idno>
            <idno type="stamp" n="LJLL" corresp="SORBONNE-UNIVERSITE">Laboratoire Jacques-Louis Lions</idno>
            <idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</idno>
            <idno type="stamp" n="DIEUDONNE-EDP-AN" corresp="DIEUDONNE">Laboratoire J.A. Dieudonné - UMR 7351 - EDP et Analyse Numérique</idno>
            <idno type="stamp" n="UPMC_POLE_1" corresp="UPMC">UPMC Pôle 1</idno>
            <idno type="stamp" n="UNIV-COTEDAZUR">Université Côte d'Azur</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="UNIV-PARIS">Université Paris Cité</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="TEST-NICE">test nice</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="invited" n="0">No</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
            <note type="proceedings" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Vertex Approximate Gradient Scheme for Hybrid Dimensional Two-Phase Darcy Flows in Fractured Porous Media </title>
                <author role="aut">
                  <persName>
                    <forename type="first">Konstantin</forename>
                    <surname>Brenner</surname>
                  </persName>
                  <idno type="halauthorid">509189-0</idno>
                  <orgName ref="#struct-168891"/>
                  <affiliation ref="#struct-168891"/>
                  <affiliation ref="#struct-199970"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Mayya</forename>
                    <surname>Groza</surname>
                  </persName>
                  <email type="md5">9e93eda3848ad8a054c50c72042e190a</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="numeric">981962</idno>
                  <idno type="halauthorid" notation="string">782233-981962</idno>
                  <orgName ref="#struct-168891"/>
                  <affiliation ref="#struct-199970"/>
                  <affiliation ref="#struct-168891"/>
                </author>
                <author role="crp">
                  <persName>
                    <forename type="first">Cindy</forename>
                    <surname>Guichard</surname>
                  </persName>
                  <email type="md5">841cd20eaf370dd8bab865011d9741c4</email>
                  <email type="domain">ljll.math.upmc.fr</email>
                  <idno type="idhal" notation="string">cindy-guichard-26</idno>
                  <idno type="idhal" notation="numeric">1115859</idno>
                  <idno type="halauthorid" notation="string">513465-1115859</idno>
                  <idno type="IDREF">https://www.idref.fr/158768493</idno>
                  <orgName ref="#struct-454317"/>
                  <affiliation ref="#struct-454317"/>
                  <affiliation ref="#struct-25"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Roland</forename>
                    <surname>Masson</surname>
                  </persName>
                  <email type="md5">ef118128bac0e07bb86886f24e6fdcf4</email>
                  <email type="domain">univ-cotedazur.fr</email>
                  <idno type="idhal" notation="string">roland-masson</idno>
                  <idno type="idhal" notation="numeric">21126</idno>
                  <idno type="halauthorid" notation="string">13248-21126</idno>
                  <idno type="IDREF">https://www.idref.fr/035818689</idno>
                  <idno type="ORCID">https://orcid.org/0009-0006-8713-3069</idno>
                  <orgName ref="#struct-168891"/>
                  <affiliation ref="#struct-199970"/>
                  <affiliation ref="#struct-168891"/>
                </author>
              </analytic>
              <monogr>
                <meeting>
                  <title>The International Symposium of Finite Volumes for Complex Applications VII</title>
                  <date type="start">2014-06-15</date>
                  <date type="end">2014-06-20</date>
                  <settlement>Berlin</settlement>
                  <country key="DE">Germany</country>
                </meeting>
                <imprint>
                  <biblScope unit="serie">Finite Volumes for Complex Applications VII- Elliptic, Parabolic and Hyperbolic Problems</biblScope>
                  <date type="datePub">2014</date>
                </imprint>
              </monogr>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="math">Mathematics [math]</classCode>
              <classCode scheme="halTypology" n="COMM">Conference papers</classCode>
              <classCode scheme="halOldTypology" n="COMM">Conference papers</classCode>
              <classCode scheme="halTreeTypology" n="COMM">Conference papers</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>This paper presents the Vertex Approximate Gradient (VAG) discretization of a two-phase Darcy flow in discrete fracture networks (DFN) taking into account the mass exchange between the matrix and the fracture. We consider the asymptotic model for which the fractures are represented as interfaces of codimension one immersed in the matrix domain with continuous pressures at the matrix fracture interface. Compared with Control Volume Finite Element (CVFE) approaches, the VAG scheme has the advantage to avoid the mixing of the fracture and matrix rocktypes at the interfaces between the matrix and the fractures, while keeping the low cost of a nodal discretization on unstructured meshes. The convergence of the scheme is proved under the assumption that the relative permeabilities are bounded from below by a strictly positive constant but cover the case of discontinuous capillary pressures. The efficiency of our approach compared with CVFE discretizations is shown on a 3D fracture network with very low matrix permeability. </p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-168891" status="OLD">
          <idno type="RNSR">201121214R</idno>
          <orgName>COmplex Flows For Energy and Environment</orgName>
          <orgName type="acronym">COFFEE</orgName>
          <date type="start">2013-01-01</date>
          <date type="end">2023-12-31</date>
          <desc>
            <address>
              <addrLine>2004 route des Lucioles - BP 93 06902 Sophia Antipolis Cedex, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/coffee</ref>
          </desc>
          <listRelation>
            <relation active="#struct-34586" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation name="UMR7351" active="#struct-199970" type="direct"/>
            <relation active="#struct-117617" type="indirect"/>
            <relation name="UMR7351" active="#struct-441569" type="indirect"/>
            <relation active="#struct-1039632" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-199970" status="VALID">
          <idno type="IdRef">060325887</idno>
          <idno type="RNSR">201220430J</idno>
          <idno type="ROR">https://ror.org/0274zdr66</idno>
          <orgName>Laboratoire Jean Alexandre Dieudonné</orgName>
          <orgName type="acronym">LJAD</orgName>
          <date type="start">2012-01-01</date>
          <desc>
            <address>
              <addrLine>Université Côte d'Azur U.M.R. no 7351 du C.N.R.S. Parc Valrose 06108 Nice Cedex 02 France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://math.unice.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-117617" type="direct"/>
            <relation name="UMR7351" active="#struct-441569" type="direct"/>
            <relation active="#struct-1039632" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-454317" status="OLD">
          <idno type="RNSR">201221061V</idno>
          <orgName>Numerical Analysis, Geophysics and Ecology</orgName>
          <orgName type="acronym">ANGE</orgName>
          <date type="start">2016-01-01</date>
          <date type="end">2017-12-31</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/ange</ref>
          </desc>
          <listRelation>
            <relation active="#struct-25" type="direct"/>
            <relation active="#struct-93591" type="indirect"/>
            <relation active="#struct-300301" type="indirect"/>
            <relation name="UMR7598" active="#struct-441569" type="indirect"/>
            <relation active="#struct-454310" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-25" status="OLD">
          <idno type="RNSR">199712644L</idno>
          <orgName>Laboratoire Jacques-Louis Lions</orgName>
          <orgName type="acronym">LJLL</orgName>
          <desc>
            <address>
              <addrLine>Université Pierre et Marie Curie, 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-93591" type="direct"/>
            <relation active="#struct-300301" type="direct"/>
            <relation name="UMR7598" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-34586" status="VALID">
          <idno type="RNSR">198318250R</idno>
          <idno type="ROR">https://ror.org/01nzkaw91</idno>
          <orgName>Centre Inria d'Université Côte d'Azur</orgName>
          <desc>
            <address>
              <addrLine>2004 route des Lucioles BP 93 06902 Sophia Antipolis</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/sophia/</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="institution" xml:id="struct-117617" status="VALID">
          <idno type="IdRef">026403498</idno>
          <idno type="ISNI">0000000123372892</idno>
          <idno type="ROR">https://ror.org/02k9vew78</idno>
          <orgName>Université Nice Sophia Antipolis (1965 - 2019)</orgName>
          <orgName type="acronym">UNS</orgName>
          <date type="start">1965-10-23</date>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>Parc Valrose, 06100 Nice</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://unice.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="regroupinstitution" xml:id="struct-1039632" status="VALID">
          <idno type="IdRef">241035694</idno>
          <idno type="ROR">https://ror.org/019tgvf94</idno>
          <orgName>Université Côte d'Azur</orgName>
          <orgName type="acronym">UniCA</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>Parc Valrose, 28, avenue Valrose 06108 Nice Cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://univ-cotedazur.fr</ref>
          </desc>
        </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-300301" status="OLD">
          <idno type="IdRef">027542084</idno>
          <idno type="ISNI">0000000121514068</idno>
          <idno type="ROR">https://ror.org/02n7qrg46</idno>
          <orgName>Université Paris Diderot - Paris 7</orgName>
          <orgName type="acronym">UPD7</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>5 rue Thomas-Mann - 75205 Paris cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-paris-diderot.fr</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>
      </listOrg>
    </back>
  </text>
</TEI>