<?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-00922835</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="2026-05-19T12:26:19+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Three-points interfacial quadrature for geometrical source terms on nonuniform grids. Application to finite volume schemes for parameter-dependent differential equations.</title>
            <author role="aut">
              <persName>
                <forename type="first">Theodoros</forename>
                <surname>Katsaounis</surname>
              </persName>
              <email type="md5">abc82dcd484c68c68772407e858a309b</email>
              <email type="domain">tem.uoc.gr</email>
              <idno type="idhal" notation="numeric">868748</idno>
              <idno type="halauthorid" notation="string">451678-868748</idno>
              <affiliation ref="#struct-1005630"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Chiara</forename>
                <surname>Simeoni</surname>
              </persName>
              <email type="md5">ff5493b403868bff0425e38753c2c7fc</email>
              <email type="domain">unice.fr</email>
              <idno type="idhal" notation="string">chiara-simeoni</idno>
              <idno type="idhal" notation="numeric">183475</idno>
              <idno type="halauthorid" notation="string">19732-183475</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-7733-4645</idno>
              <affiliation ref="#struct-242004"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Chiara</forename>
                <surname>Simeoni</surname>
              </persName>
              <email type="md5">0bdea4ddc375aeeb299604b431a15ecc</email>
              <email type="domain">univ-cotedazur.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2013-12-31 00:05:59</date>
              <date type="whenModified">2025-01-06 12:22:03</date>
              <date type="whenReleased">2013-12-31 18:34:00</date>
              <date type="whenProduced">2012</date>
              <date type="whenEndEmbargoed">2013-12-31</date>
              <ref type="file" target="https://hal.science/hal-00922835v1/document">
                <date notBefore="2013-12-31"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-00922835v1/file/Katsaounis_Simeoni_2012.pdf" id="file-922835-1073075">
                <date notBefore="2013-12-31"/>
              </ref>
              <ref type="externalLink" target="http://preprints.acmac.uoc.gr/59/1/acmac-0059.pdf"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="188318">
                <persName>
                  <forename>Chiara</forename>
                  <surname>Simeoni</surname>
                </persName>
                <email type="md5">0bdea4ddc375aeeb299604b431a15ecc</email>
                <email type="domain">univ-cotedazur.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00922835</idno>
            <idno type="halUri">https://hal.science/hal-00922835</idno>
            <idno type="halBibtex">katsaounis:hal-00922835</idno>
            <idno type="halRefHtml">&lt;i&gt;Calcolo&lt;/i&gt;, 2012, 49 (3), pp.149-176. &lt;a target="_blank" href="https://dx.doi.org/10.1007/s10092-011-0049-6"&gt;&amp;#x27E8;10.1007/s10092-011-0049-6&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Calcolo, 2012, 49 (3), pp.149-176. &amp;#x27E8;10.1007/s10092-011-0049-6&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-922835-1073075"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="DIEUDONNE">Laboratoire Jean-Alexandre Dieudonné</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="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</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">Three-points interfacial quadrature for geometrical source terms on nonuniform grids. Application to finite volume schemes for parameter-dependent differential equations.</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Theodoros</forename>
                    <surname>Katsaounis</surname>
                  </persName>
                  <email type="md5">abc82dcd484c68c68772407e858a309b</email>
                  <email type="domain">tem.uoc.gr</email>
                  <idno type="idhal" notation="numeric">868748</idno>
                  <idno type="halauthorid" notation="string">451678-868748</idno>
                  <affiliation ref="#struct-1005630"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Chiara</forename>
                    <surname>Simeoni</surname>
                  </persName>
                  <email type="md5">ff5493b403868bff0425e38753c2c7fc</email>
                  <email type="domain">unice.fr</email>
                  <idno type="idhal" notation="string">chiara-simeoni</idno>
                  <idno type="idhal" notation="numeric">183475</idno>
                  <idno type="halauthorid" notation="string">19732-183475</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-7733-4645</idno>
                  <affiliation ref="#struct-242004"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">11472</idno>
                <idno type="issn">0008-0624</idno>
                <idno type="eissn">1126-5434</idno>
                <title level="j">Calcolo</title>
                <imprint>
                  <publisher>Springer Verlag</publisher>
                  <biblScope unit="volume">49</biblScope>
                  <biblScope unit="issue">3</biblScope>
                  <biblScope unit="pp">149-176</biblScope>
                  <date type="datePub">2012</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1007/s10092-011-0049-6</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">nonuniform grids</term>
                <term xml:lang="en">geometrical source terms</term>
                <term xml:lang="en">finite volume schemes</term>
                <term xml:lang="en">optimal convergence rates</term>
                <term xml:lang="en">consistency</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>This paper deals with numerical (finite volume) approximations, on nonuniform meshes, for ordinary differential equations with parameter-dependent fields. Appropriate discretizations are constructed over the space of parameters, in order to guarantee the consistency in presence of variable cells' size, for which $L^p$-error estimates, $1\le p &lt; +\infty$, are proven. Besides, a suitable notion of (weak) regularity for nonuniform meshes is introduced in the most general case, to compensate possibly reduced consistency conditions, and the optimality of the convergence rates with respect to the regularity assumptions on the problem's data is precisely discussed. This analysis attempts to provide a basic theoretical framework for the numerical simulation on unstructured grids (also generated by adaptive algorithms) of a wide class of mathematical models for real systems (geophysical flows, biological and chemical processes, population dynamics).</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="institution" xml:id="struct-1005630" status="INCOMING">
          <orgName>Department of Mathematics and Applied Mathematics, University of Crete (Heraklion, Greece)</orgName>
          <desc>
            <address>
              <country key="GR"/>
            </address>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-242004" status="VALID">
          <orgName>Department of Information Engineering, Computer Science and Mathematics = Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica [L'Aquila]</orgName>
          <orgName type="acronym">DISIM</orgName>
          <desc>
            <address>
              <addrLine>Università degli Studi dell'Aquila, Via Vetoio, I-67100 L'Aquila</addrLine>
              <country key="IT"/>
            </address>
            <ref type="url">https://www.disim.univaq.it/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301597" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-301597" status="VALID">
          <idno type="IdRef">03353411X</idno>
          <idno type="ISNI">0000000417572611</idno>
          <idno type="ROR">https://ror.org/01j9p1r26</idno>
          <idno type="Wikidata">Q1494671</idno>
          <orgName>Università degli Studi dell'Aquila = University of L'Aquila = Université de L'Aquila</orgName>
          <orgName type="acronym">UNIVAQ</orgName>
          <date type="start">1952-01-01</date>
          <desc>
            <address>
              <addrLine>Via Giovanni Di Vincenzo 16/B, 67100 L'Aquila</addrLine>
              <country key="IT"/>
            </address>
            <ref type="url">https://www.univaq.it/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>