<?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-01294243</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="2026-05-19T19:25:19+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">A sixth-order finite volume scheme for the steady-state incompressible Stokes equations on staggered unstructured meshes</title>
            <author role="crp">
              <persName>
                <forename type="first">Ricardo</forename>
                <surname>Costa</surname>
              </persName>
              <idno type="idhal" notation="numeric">980298</idno>
              <idno type="halauthorid" notation="string">852298-980298</idno>
              <affiliation ref="#struct-103580"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Stéphane</forename>
                <surname>Clain</surname>
              </persName>
              <email type="md5">ef20f78dea543b2df018cfe082e6f957</email>
              <email type="domain">math.uminho.pt</email>
              <idno type="idhal" notation="string">stephane-clain</idno>
              <idno type="idhal" notation="numeric">5127</idno>
              <idno type="halauthorid" notation="string">1570-5127</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-2295-5118</idno>
              <idno type="IDREF">https://www.idref.fr/139497617</idno>
              <affiliation ref="#struct-103580"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Gaspar</forename>
                <surname>Machado</surname>
              </persName>
              <email type="md5">bb1593eb30a41edf8bcb829ca26b2c99</email>
              <email type="domain">math.uminho.pt</email>
              <idno type="idhal" notation="numeric">911820</idno>
              <idno type="halauthorid" notation="string">589463-911820</idno>
              <affiliation ref="#struct-103580"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Stephane</forename>
                <surname>Clain</surname>
              </persName>
              <email type="md5">714f486a8f952a675154bd3331260895</email>
              <email type="domain">gmail.com</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2016-03-28 20:55:47</date>
              <date type="whenModified">2024-04-22 10:10:57</date>
              <date type="whenReleased">2016-03-30 10:13:39</date>
              <date type="whenProduced">2016-03-28</date>
              <date type="whenEndEmbargoed">2016-03-28</date>
              <ref type="file" target="https://hal.science/hal-01294243v1/document">
                <date notBefore="2016-03-28"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-01294243v1/file/main.pdf" id="file-1294243-1375701">
                <date notBefore="2016-03-28"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="131685">
                <persName>
                  <forename>Stephane</forename>
                  <surname>Clain</surname>
                </persName>
                <email type="md5">714f486a8f952a675154bd3331260895</email>
                <email type="domain">gmail.com</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01294243</idno>
            <idno type="halUri">https://hal.science/hal-01294243</idno>
            <idno type="halBibtex">costa:hal-01294243</idno>
            <idno type="halRefHtml">2016</idno>
            <idno type="halRef">2016</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-1294243-1375701"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
          </seriesStmt>
          <notesStmt/>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">A sixth-order finite volume scheme for the steady-state incompressible Stokes equations on staggered unstructured meshes</title>
                <author role="crp">
                  <persName>
                    <forename type="first">Ricardo</forename>
                    <surname>Costa</surname>
                  </persName>
                  <idno type="idhal" notation="numeric">980298</idno>
                  <idno type="halauthorid" notation="string">852298-980298</idno>
                  <affiliation ref="#struct-103580"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Stéphane</forename>
                    <surname>Clain</surname>
                  </persName>
                  <email type="md5">ef20f78dea543b2df018cfe082e6f957</email>
                  <email type="domain">math.uminho.pt</email>
                  <idno type="idhal" notation="string">stephane-clain</idno>
                  <idno type="idhal" notation="numeric">5127</idno>
                  <idno type="halauthorid" notation="string">1570-5127</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-2295-5118</idno>
                  <idno type="IDREF">https://www.idref.fr/139497617</idno>
                  <affiliation ref="#struct-103580"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Gaspar</forename>
                    <surname>Machado</surname>
                  </persName>
                  <email type="md5">bb1593eb30a41edf8bcb829ca26b2c99</email>
                  <email type="domain">math.uminho.pt</email>
                  <idno type="idhal" notation="numeric">911820</idno>
                  <idno type="halauthorid" notation="string">589463-911820</idno>
                  <affiliation ref="#struct-103580"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Stokes equations</term>
                <term xml:lang="en">incompressible fluid</term>
                <term xml:lang="en">finite volume</term>
                <term xml:lang="en">high-order scheme</term>
                <term xml:lang="en">preconditioning</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>We propose a new sixth-order finite volume scheme to solve the bidimensional linear steady-state Stokes problem on staggered unstructured meshes and complex geometries. The method is based on several classes of polynomial reconstructions to accurately evaluate the diffusive fluxes, the pressure gradient, and the velocity divergence. The main difficulty is to handle the div-grad duality to avoid numerical locking and oscillations. A new preconditioning technique based on the construction of a pseudo-inverse matrix is also proposed to dramatically reduce the computational effort. Several numerical simulations are carried out to highlight the performance of the new method.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-103580" status="VALID">
          <orgName>Centro de Matemática [Minho]</orgName>
          <orgName type="acronym">CMAT</orgName>
          <desc>
            <address>
              <addrLine>Universidade do Minho Campus de Gualtar, 4710-057 Braga</addrLine>
              <country key="PT"/>
            </address>
            <ref type="url">http://www.cmat.uminho.pt/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300854" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300854" status="VALID">
          <orgName>Universidade do Minho = University of Minho  [Braga]</orgName>
          <date type="start">2016-11-23</date>
          <desc>
            <address>
              <addrLine>Largo do Paço, 4704-553 Braga</addrLine>
              <country key="PT"/>
            </address>
            <ref type="url">https://www.uminho.pt</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>