<?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-04033438v2</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="2026-05-21T21:06:14+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Robust energy a posteriori estimates for nonlinear elliptic problems</title>
            <author role="crp">
              <persName>
                <forename type="first">André</forename>
                <surname>Harnist</surname>
              </persName>
              <email type="md5">cbb42a40bdc42f6dc70b3c05bfb90c48</email>
              <email type="domain">outlook.fr</email>
              <idno type="idhal" notation="string">andre-harnist</idno>
              <idno type="idhal" notation="numeric">1112034</idno>
              <idno type="halauthorid" notation="string">1812141-1112034</idno>
              <affiliation ref="#struct-454687"/>
              <affiliation ref="#struct-51621"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Koondanibha</forename>
                <surname>Mitra</surname>
              </persName>
              <email type="md5">7e23a1fce9bd3b8a059922ab39c3535d</email>
              <email type="domain">uhasselt.be</email>
              <idno type="idhal" notation="numeric">1238290</idno>
              <idno type="halauthorid" notation="string">2272719-1238290</idno>
              <affiliation ref="#struct-469275"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Ari</forename>
                <surname>Rappaport</surname>
              </persName>
              <email type="md5">a4cebdf398ac9b41f8de08c6a443611f</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">ari-rappaport</idno>
              <idno type="idhal" notation="numeric">1256645</idno>
              <idno type="halauthorid" notation="string">2759701-1256645</idno>
              <idno type="ORCID">https://orcid.org/0009-0002-5796-1104</idno>
              <idno type="IDREF">https://www.idref.fr/279147430</idno>
              <affiliation ref="#struct-454687"/>
              <affiliation ref="#struct-51621"/>
            </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>
              <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>
              <affiliation ref="#struct-454687"/>
              <affiliation ref="#struct-51621"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>André</forename>
                <surname>Harnist</surname>
              </persName>
              <email type="md5">cbb42a40bdc42f6dc70b3c05bfb90c48</email>
              <email type="domain">outlook.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2023-03-17 09:25:27</date>
            </edition>
            <edition n="v2" type="current">
              <date type="whenSubmitted">2023-05-26 14:43:27</date>
              <date type="whenModified">2026-03-13 15:40:02</date>
              <date type="whenReleased">2023-05-26 22:01:42</date>
              <date type="whenProduced">2023-05-26</date>
              <date type="whenEndEmbargoed">2023-05-26</date>
              <ref type="file" target="https://hal.science/hal-04033438v2/document">
                <date notBefore="2023-05-26"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-04033438v2/file/nlde.pdf" id="file-4107823-3576624">
                <date notBefore="2023-05-26"/>
              </ref>
            </edition>
            <edition n="v3">
              <date type="whenSubmitted">2024-06-10 11:34:14</date>
            </edition>
            <edition n="v4">
              <date type="whenSubmitted">2026-04-07 11:29:01</date>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="523202">
                <persName>
                  <forename>André</forename>
                  <surname>Harnist</surname>
                </persName>
                <email type="md5">cbb42a40bdc42f6dc70b3c05bfb90c48</email>
                <email type="domain">outlook.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-04033438</idno>
            <idno type="halUri">https://hal.science/hal-04033438</idno>
            <idno type="halBibtex">harnist:hal-04033438</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-4107823-3576624"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt/>
          <notesStmt/>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Robust energy a posteriori estimates for nonlinear elliptic problems</title>
                <author role="crp">
                  <persName>
                    <forename type="first">André</forename>
                    <surname>Harnist</surname>
                  </persName>
                  <email type="md5">cbb42a40bdc42f6dc70b3c05bfb90c48</email>
                  <email type="domain">outlook.fr</email>
                  <idno type="idhal" notation="string">andre-harnist</idno>
                  <idno type="idhal" notation="numeric">1112034</idno>
                  <idno type="halauthorid" notation="string">1812141-1112034</idno>
                  <affiliation ref="#struct-454687"/>
                  <affiliation ref="#struct-51621"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Koondanibha</forename>
                    <surname>Mitra</surname>
                  </persName>
                  <email type="md5">7e23a1fce9bd3b8a059922ab39c3535d</email>
                  <email type="domain">uhasselt.be</email>
                  <idno type="idhal" notation="numeric">1238290</idno>
                  <idno type="halauthorid" notation="string">2272719-1238290</idno>
                  <affiliation ref="#struct-469275"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Ari</forename>
                    <surname>Rappaport</surname>
                  </persName>
                  <email type="md5">a4cebdf398ac9b41f8de08c6a443611f</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">ari-rappaport</idno>
                  <idno type="idhal" notation="numeric">1256645</idno>
                  <idno type="halauthorid" notation="string">2759701-1256645</idno>
                  <idno type="ORCID">https://orcid.org/0009-0002-5796-1104</idno>
                  <idno type="IDREF">https://www.idref.fr/279147430</idno>
                  <affiliation ref="#struct-454687"/>
                  <affiliation ref="#struct-51621"/>
                </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>
                  <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>
                  <affiliation ref="#struct-454687"/>
                  <affiliation ref="#struct-51621"/>
                </author>
              </analytic>
              <monogr>
                <imprint>
                  <date type="datePub">2023-03-17</date>
                </imprint>
              </monogr>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Nonlinear elliptic problem</term>
                <term xml:lang="en">Finite elements</term>
                <term xml:lang="en">Iterative linearization</term>
                <term xml:lang="en">Energy difference</term>
                <term xml:lang="en">A posteriori error estimate</term>
                <term xml:lang="en">Robustness</term>
                <term xml:lang="en">Equilibrated flux reconstruction</term>
              </keywords>
              <classCode scheme="halDomain" n="math.math-na">Mathematics [math]/Numerical Analysis [math.NA]</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>In this paper, we design a posteriori estimates for finite element approximations of nonlinear elliptic problems satisfying strong-monotonicity and Lipschitz-continuity properties. These estimates include, and build on, any iterative linearization method that satisfies a few clearly identified assumptions; this encompasses the Picard, Newton, and Zarantonello linearizations. The estimates give a guaranteed upper bound on an augmented energy difference (reliability with constant one), as well as a lower bound (efficiency up to a generic constant). We prove that for the Zarantonello linearization, this generic constant only depends on the space dimension, the mesh shape regularity, and possibly the approximation polynomial degree in four or more space dimensions, making the estimates robust with respect to the strength of the nonlinearity. For the other linearizations, there is only a computable dependence on the local variation of the linearization operators. We also derive similar estimates for the energy difference. Numerical experiments illustrate and validate the theoretical results, for both smooth and singular solutions.</p>
            </abstract>
          </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-469275" status="VALID">
          <idno type="ROR">https://ror.org/04nbhqj75</idno>
          <orgName>Hasselt University</orgName>
          <orgName type="acronym">UHasselt</orgName>
          <desc>
            <address>
              <addrLine>Campus Hasselt | Martelarenlaan 42 | BE3500 HasseltCampus Diepenbeek | Agoralaan gebouw D | BE3590 Diepenbeek</addrLine>
              <country key="BE"/>
            </address>
            <ref type="url">http://www.uhasselt.be/</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>
      </listOrg>
    </back>
  </text>
</TEI>