<?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-00783068</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="2026-05-01T21:48:16+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">A review of recent advances in discretization methods, a posteriori error analysis, and adaptive algorithms for numerical modeling in geosciences</title>
            <author role="aut">
              <persName>
                <forename type="first">Daniele Antonio</forename>
                <surname>Di Pietro</surname>
              </persName>
              <email type="md5">1e1a4362deafeafb7a66ef3068c29689</email>
              <email type="domain">ifp.fr</email>
              <idno type="idhal" notation="string">ddp</idno>
              <idno type="idhal" notation="numeric">14727</idno>
              <idno type="halauthorid" notation="string">6742-14727</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-0959-8830</idno>
              <idno type="IDREF">https://www.idref.fr/158727800</idno>
              <affiliation ref="#struct-631"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Martin</forename>
                <surname>Vohralík</surname>
              </persName>
              <email type="md5">5186f37fe1692565a2ad481f004af39b</email>
              <email type="domain">inria.fr</email>
              <ptr type="url" target="https://who.rocq.inria.fr/Martin.Vohralik/"/>
              <idno type="idhal" notation="string">vohralik</idno>
              <idno type="idhal" notation="numeric">739353</idno>
              <idno type="halauthorid" notation="string">45950-739353</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-8838-7689</idno>
              <idno type="IDREF">https://www.idref.fr/088621596</idno>
              <orgName ref="#struct-300009"/>
              <affiliation ref="#struct-182203"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Daniele Antonio</forename>
                <surname>Di Pietro</surname>
              </persName>
              <email type="md5">ef574605871c7e3e9a92970f9ac849f5</email>
              <email type="domain">umontpellier.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2013-01-31 12:38:29</date>
              <date type="whenWritten">2013-01-31</date>
              <date type="whenModified">2025-02-28 03:25:31</date>
              <date type="whenReleased">2013-01-31 16:25:23</date>
              <date type="whenProduced">2014-06-11</date>
              <date type="whenEndEmbargoed">2013-01-31</date>
              <ref type="file" target="https://hal.science/hal-00783068v1/document">
                <date notBefore="2013-01-31"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-00783068v1/file/OGST.pdf" id="file-783068-746041">
                <date notBefore="2013-01-31"/>
              </ref>
              <ref type="externalLink" target="https://ogst.ifpenergiesnouvelles.fr/articles/ogst/pdf/2014/04/ogst130026.pdf"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="128537">
                <persName>
                  <forename>Daniele Antonio</forename>
                  <surname>Di Pietro</surname>
                </persName>
                <email type="md5">ef574605871c7e3e9a92970f9ac849f5</email>
                <email type="domain">umontpellier.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00783068</idno>
            <idno type="halUri">https://hal.science/hal-00783068</idno>
            <idno type="halBibtex">dipietro:hal-00783068</idno>
            <idno type="halRefHtml">&lt;i&gt;Oil &amp; Gas Science and Technology - Revue d'IFP Energies nouvelles&lt;/i&gt;, 2014, 69 (4), pp.701-730. &lt;a target="_blank" href="https://dx.doi.org/10.2516/ogst/2013158"&gt;&amp;#x27E8;10.2516/ogst/2013158&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Oil &amp; Gas Science and Technology - Revue d'IFP Energies nouvelles, 2014, 69 (4), pp.701-730. &amp;#x27E8;10.2516/ogst/2013158&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-783068-746041"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <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="UNIV-MONTP2">Université Montpellier II - Sciences et Techniques du Languedoc</idno>
            <idno type="stamp" n="INRIA-ROCQ">INRIA Paris - Rocquencourt</idno>
            <idno type="stamp" n="I3M_UMR5149">Institut de Mathématiques et de Modélisation de Montpellier</idno>
            <idno type="stamp" n="IMMM">Institut de Mathématiques et de Modélisation de Montpellier</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="IMAG-MONTPELLIER">Institut Montpelliérain Alexander Grothendieck</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</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="OGST">Oil &amp; Gas Science and Technology – Revue d’IFP Energies nouvelles</idno>
            <idno type="stamp" n="UNIV-MONTPELLIER">Université de Montpellier</idno>
            <idno type="stamp" n="INRIA-300009">Inria 300009</idno>
            <idno type="stamp" n="UM1-UM2" corresp="UNIV-MONTPELLIER">Université Montpellier 1 - Université Montpellier 2</idno>
            <idno type="stamp" n="UM-2015-2021" corresp="UNIV-MONTPELLIER">Université de Montpellier (2015-2021)</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">A review of recent advances in discretization methods, a posteriori error analysis, and adaptive algorithms for numerical modeling in geosciences</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Daniele Antonio</forename>
                    <surname>Di Pietro</surname>
                  </persName>
                  <email type="md5">1e1a4362deafeafb7a66ef3068c29689</email>
                  <email type="domain">ifp.fr</email>
                  <idno type="idhal" notation="string">ddp</idno>
                  <idno type="idhal" notation="numeric">14727</idno>
                  <idno type="halauthorid" notation="string">6742-14727</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-0959-8830</idno>
                  <idno type="IDREF">https://www.idref.fr/158727800</idno>
                  <affiliation ref="#struct-631"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Martin</forename>
                    <surname>Vohralík</surname>
                  </persName>
                  <email type="md5">5186f37fe1692565a2ad481f004af39b</email>
                  <email type="domain">inria.fr</email>
                  <ptr type="url" target="https://who.rocq.inria.fr/Martin.Vohralik/"/>
                  <idno type="idhal" notation="string">vohralik</idno>
                  <idno type="idhal" notation="numeric">739353</idno>
                  <idno type="halauthorid" notation="string">45950-739353</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-8838-7689</idno>
                  <idno type="IDREF">https://www.idref.fr/088621596</idno>
                  <orgName ref="#struct-300009"/>
                  <affiliation ref="#struct-182203"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="OLD">1865</idno>
                <idno type="issn">1294-4475</idno>
                <idno type="eissn">1953-8189</idno>
                <title level="j">Oil &amp; Gas Science and Technology - Revue d'IFP Energies nouvelles</title>
                <imprint>
                  <publisher>Institut Français du Pétrole (IFP)</publisher>
                  <biblScope unit="volume">69</biblScope>
                  <biblScope unit="issue">4</biblScope>
                  <biblScope unit="pp">701-730</biblScope>
                  <date type="datePub">2014-06-11</date>
                </imprint>
              </monogr>
              <idno type="doi">10.2516/ogst/2013158</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">fully adaptive algorithms</term>
                <term xml:lang="en">a posteriori error estimates</term>
                <term xml:lang="en">discontinuous Galerkin methods</term>
                <term xml:lang="en">finite volume methods</term>
                <term xml:lang="en">numerical methods for diffusive terms</term>
              </keywords>
              <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>Two research subjects in geosciences which lately underwent significant progress are treated in this review. In the first part we focus on one key ingredient for the numerical approximation of the Darcy flow problem, namely the discretization of diffusion terms on general polygonal/polyhedral meshes. We present different schemes and discuss in detail their fundamental numerical properties such as stability, consistency, and robustness. The second part of the paper is devoted to error control and adaptivity for model geosciences problems. We present the available a posteriori estimates guaranteeing the maximal overall error and show how the different error components can be identified. These estimates are used to formulate adaptive stopping criteria for linear and nonlinear solvers, time step choice adjustment, and adaptive mesh refinement. Numerical experiments illustrate such entirely adaptive algorithms.</p>
            </abstract>
            <particDesc>
              <org type="consortium">ERT project "Enhanced oil recovery and geological sequestration of CO : mesh 2 adaptivity</org>
              <org type="consortium">a posteriori error control</org>
              <org type="consortium">and other advanced techniques" (IFP/LJLL)</org>
            </particDesc>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-631" status="OLD">
          <orgName>Institut de Mathématiques et de Modélisation de Montpellier</orgName>
          <orgName type="acronym">I3M</orgName>
          <desc>
            <address>
              <addrLine>Case Courrier 051 Place Eugène Bataillon 34095 MONTPELLIER CEDEX 5</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.math.univ-montp2.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-92690" type="direct"/>
            <relation active="#struct-410122" type="direct"/>
            <relation name="UMR5149" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-182203" status="OLD">
          <idno type="RNSR">201221277E</idno>
          <orgName>Environmental Modeling, Optimization and Programming Models</orgName>
          <orgName type="acronym">POMDAPI</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/pomdapi</ref>
          </desc>
          <listRelation>
            <relation active="#struct-86790" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-92690" status="OLD">
          <orgName>Université Montpellier 2 - Sciences et Techniques</orgName>
          <orgName type="acronym">UM2</orgName>
          <date type="end">2014-12-31</date>
          <desc>
            <address>
              <addrLine>Place Eugène Bataillon - 34095 Montpellier cedex 5</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-montp2.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-410122" status="OLD">
          <idno type="ISNI">0000000120970141</idno>
          <idno type="ROR">https://ror.org/051escj72</idno>
          <orgName>Université de Montpellier</orgName>
          <orgName type="acronym">UM</orgName>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <addrLine>163 rue Auguste Broussonnet - 34090 Montpellier</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.umontpellier.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="laboratory" xml:id="struct-86790" status="OLD">
          <orgName>Inria Paris-Rocquencourt</orgName>
          <date type="end">2016-03-30</date>
          <desc>
            <address>
              <addrLine>INRIA Rocquencourt : Domaine de Voluceau, Rocquencourt B.P. 105 78153 le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/paris-rocquencourt</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>
      </listOrg>
    </back>
  </text>
</TEI>