Publikation:

An adaptive certified space-time reduced basis method for nonsmooth parabolic partial differential equations

Vorschaubild

Dateien

Zu diesem Dokument gibt es keine Dateien.

Datum

2022

Autor:innen

Herausgeber:innen

Kontakt

ISSN der Zeitschrift

Electronic ISSN

ISBN

Bibliografische Daten

Verlag

Schriftenreihe

Auflagebezeichnung

URI (zitierfähiger Link)
DOI (zitierfähiger Link)
ArXiv-ID
http://arxiv.org/abs/2212.13744

Internationale Patentnummer

Angaben zur Forschungsförderung

Projekt

Open Access-Veröffentlichung

Sammlungen

Mathematik und Statistik: Publikationen
Core Facility der Universität Konstanz

Gesperrt bis

Titel in einer weiteren Sprache

Publikationstyp
Preprint
Publikationsstatus
Published

Erschienen in

Zusammenfassung

In this paper, a nonsmooth semilinear parabolic partial differential equation (PDE) is considered. For a reduced basis (RB) approach, a space-time formulation is used to develop a certified a-posteriori error estimator. This error estimator is adopted to the presence of the discrete empirical interpolation method (DEIM) as approximation technique for the nonsmoothness. The separability of the estimated error into an RB and a DEIM part then guides the development of an adaptive RB-DEIM algorithm, combining both offline phases into one. Numerical experiments show the capabilities of this novel approach in comparison with classical RB and RB-DEIM approaches.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Nonsmooth parabolic equations, space-time discretization, reduced basis, discrete empirical interpolation, a-posteriori error estimation, semismooth Newton

Konferenz

Rezension
undefined / . - undefined, undefined

Forschungsvorhaben

Organisationseinheiten

Zeitschriftenheft

Zugehörige Datensätze in KOPS

Zitieren

ISO 690BERNREUTHER, Marco, Stefan VOLKWEIN, 2022. An adaptive certified space-time reduced basis method for nonsmooth parabolic partial differential equations
BibTex
@unpublished{Bernreuther2022-12-28T08:41:11Zadapt-59662,
  year={2022},
  title={An adaptive certified space-time reduced basis method for nonsmooth parabolic partial differential equations},
  author={Bernreuther, Marco and Volkwein, Stefan}
}
RDF
<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/59662">
    <dc:contributor>Volkwein, Stefan</dc:contributor>
    <dcterms:abstract xml:lang="eng">In this paper, a nonsmooth semilinear parabolic partial differential equation (PDE) is considered. For a reduced basis (RB) approach, a space-time formulation is used to develop a certified a-posteriori error estimator. This error estimator is adopted to the presence of the discrete empirical interpolation method (DEIM) as approximation technique for the nonsmoothness. The separability of the estimated error into an RB and a DEIM part then guides the development of an adaptive RB-DEIM algorithm, combining both offline phases into one. Numerical experiments show the capabilities of this novel approach in comparison with classical RB and RB-DEIM approaches.</dcterms:abstract>
    <dcterms:issued>2022-12-28T08:41:11Z</dcterms:issued>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2023-01-10T11:32:54Z</dcterms:available>
    <dc:contributor>Bernreuther, Marco</dc:contributor>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/59662"/>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dc:creator>Volkwein, Stefan</dc:creator>
    <dc:language>eng</dc:language>
    <dcterms:title>An adaptive certified space-time reduced basis method for nonsmooth parabolic partial differential equations</dcterms:title>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dc:rights>terms-of-use</dc:rights>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2023-01-10T11:32:54Z</dc:date>
    <dc:creator>Bernreuther, Marco</dc:creator>
  </rdf:Description>
</rdf:RDF>

Interner Vermerk

xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter

Kontakt
URL der Originalveröffentl.

Prüfdatum der URL

Prüfungsdatum der Dissertation

Finanzierungsart

Kommentar zur Publikation

Allianzlizenz
Corresponding Authors der Uni Konstanz vorhanden
Internationale Co-Autor:innen
Universitätsbibliographie
Ja
Begutachtet
Diese Publikation teilen