<?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-01581883</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="2026-05-03T04:52:25+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Assessment of Hybrid High-Order methods on curved meshes and comparison with discontinuous Galerkin methods</title>
            <author role="aut">
              <persName>
                <forename type="first">Lorenzo</forename>
                <surname>Botti</surname>
              </persName>
              <email type="md5">d879a95e7fdadc9ada95b3d732d484c5</email>
              <email type="domain">unibg.it</email>
              <idno type="idhal" notation="numeric">867415</idno>
              <idno type="halauthorid" notation="string">443652-867415</idno>
              <affiliation ref="#struct-505722"/>
            </author>
            <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-424479"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Lorenzo Alessio</forename>
                <surname>Botti</surname>
              </persName>
              <email type="md5">bd50a307b1d6bc424efd1e2924914f4f</email>
              <email type="domain">gmail.com</email>
            </editor>
            <funder ref="#projanr-41666"/>
            <funder>Agence Nationale de la Recherche through grant HHOMM (ANR-15-CE40-0005) University of Bergamo through the project ITALY – Italian TALented Young researchers</funder>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2017-09-05 11:45:12</date>
              <date type="whenModified">2024-04-26 13:38:44</date>
              <date type="whenReleased">2017-09-05 17:44:10</date>
              <date type="whenProduced">2018-10-01</date>
              <date type="whenEndEmbargoed">2017-09-05</date>
              <ref type="file" target="https://hal.science/hal-01581883v1/document">
                <date notBefore="2017-09-05"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-01581883v1/file/curvhho.pdf" id="file-1581883-1634985">
                <date notBefore="2017-09-05"/>
              </ref>
              <ref type="externalLink" target="https://hal.archives-ouvertes.fr/hal-01581883/file/curvhho.pdf"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="148937">
                <persName>
                  <forename>Lorenzo Alessio</forename>
                  <surname>Botti</surname>
                </persName>
                <email type="md5">bd50a307b1d6bc424efd1e2924914f4f</email>
                <email type="domain">gmail.com</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01581883</idno>
            <idno type="halUri">https://hal.science/hal-01581883</idno>
            <idno type="halBibtex">botti:hal-01581883</idno>
            <idno type="halRefHtml">&lt;i&gt;Journal of Computational Physics&lt;/i&gt;, 2018, 370, pp.58-84. &lt;a target="_blank" href="https://dx.doi.org/10.1016/j.jcp.2018.05.017"&gt;&amp;#x27E8;10.1016/j.jcp.2018.05.017&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Journal of Computational Physics, 2018, 370, pp.58-84. &amp;#x27E8;10.1016/j.jcp.2018.05.017&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://hal.science/licences/copyright/">Copyright - All rights reserved<ref corresp="#file-1581883-1634985"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="I3M_UMR5149">Institut de Mathématiques et de Modélisation de Montpellier</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="IMAG-MONTPELLIER">Institut Montpelliérain Alexander Grothendieck</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="MIPS">Mathématiques, Informatique, Physique et Systèmes</idno>
            <idno type="stamp" n="UNIV-MONTPELLIER">Université de Montpellier</idno>
            <idno type="stamp" n="ANR">ANR</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">Assessment of Hybrid High-Order methods on curved meshes and comparison with discontinuous Galerkin methods</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Lorenzo</forename>
                    <surname>Botti</surname>
                  </persName>
                  <email type="md5">d879a95e7fdadc9ada95b3d732d484c5</email>
                  <email type="domain">unibg.it</email>
                  <idno type="idhal" notation="numeric">867415</idno>
                  <idno type="halauthorid" notation="string">443652-867415</idno>
                  <affiliation ref="#struct-505722"/>
                </author>
                <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-424479"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">15275</idno>
                <idno type="issn">0021-9991</idno>
                <idno type="eissn">1090-2716</idno>
                <title level="j">Journal of Computational Physics</title>
                <imprint>
                  <publisher>Elsevier</publisher>
                  <biblScope unit="volume">370</biblScope>
                  <biblScope unit="pp">58-84</biblScope>
                  <date type="datePub">2018-10-01</date>
                  <date type="dateEpub">2018-05-24</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1016/j.jcp.2018.05.017</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">discontinuous Galerkin methods</term>
                <term xml:lang="en">Hybrid High-Order methods</term>
                <term xml:lang="en">curved meshes</term>
                <term xml:lang="en">Poisson problem</term>
                <term xml:lang="en">curved elements</term>
              </keywords>
              <classCode scheme="classification">MSC 2010: 65N08, 65N30, 65N12</classCode>
              <classCode scheme="halDomain" n="info.info-mo">Computer Science [cs]/Modeling and Simulation</classCode>
              <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>We propose and validate a novel extension of Hybrid High-Order (HHO) methods to meshes featuring curved elements. HHO methods are based on discrete unknowns that are broken polynomials on the mesh and its skeleton. We propose here the use of physical frame polynomials over mesh elements and reference frame polynomials over mesh faces. With this choice, the degree of face unknowns must be suitably selected in order to recover on curved meshes analogous convergence rates as on straight meshes. We provide an estimate of the optimal face polynomial degree depending on the element polynomial degree and on the so-called effective mapping order. The estimate is numerically validated through specifically crafted numerical tests. We also give effective practical indications on how to choose the face polynomial degree on more standard problems closer to real life configurations, all corroborated by numerical evidence. In the worst case scenario of dealing with randomly distorted mesh sequences it is typically sufficient to select polynomial spaces over faces only one degree higher than on the elements to obtain optimal convergence rates. All test cases are conducted considering two-and three-dimensional pure diffusion problems, and include comparisons with DG discretizations. The extension to agglomerated meshes with curved boundaries is also considered.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="department" xml:id="struct-505722" status="INCOMING">
          <orgName>Dipartimento di Ingegneria e scienze applicate</orgName>
          <desc>
            <address>
              <country key="IT"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-308253" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-424479" status="OLD">
          <idno type="ISNI">0000000404890602</idno>
          <idno type="RNSR">200311827X</idno>
          <idno type="ROR">https://ror.org/044kxby82</idno>
          <orgName>Institut Montpelliérain Alexander Grothendieck</orgName>
          <orgName type="acronym">IMAG</orgName>
          <date type="start">2015-01-01</date>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <addrLine>UMR CNRS 5149 - Université Montpellier 2, Case courrier 051, 34095 Montpellier cedex 5 - France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://imag.umontpellier.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-410122" type="direct"/>
            <relation name="UMR5149" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-308253" status="VALID">
          <orgName>Università degli Studi di Bergamo = University of Bergamo</orgName>
          <orgName type="acronym">UniBg</orgName>
          <date type="start">1968-01-01</date>
          <desc>
            <address>
              <addrLine>via Salvecchio 19 - 24129 Bergamo</addrLine>
              <country key="IT"/>
            </address>
            <ref type="url">https://www.unibg.it/</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>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-41666" status="VALID">
          <idno type="anr">ANR-15-CE40-0005</idno>
          <orgName>HHOMM</orgName>
          <desc>Méthodes hybrides d'ordre élevé sur maillages polyédriques</desc>
          <date type="start">2015</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>