A Positivity-preserving Numerical Scheme for a Nonlinear Fourth Order Parabolic System
Lade...
Dateien
Datum
2000
Autor:innen
Jüngel, Ansgar
Pinnau, René
Herausgeber:innen
ISSN der Zeitschrift
Electronic ISSN
ISBN
Bibliografische Daten
Verlag
Schriftenreihe
Auflagebezeichnung
URI (zitierfähiger Link)
Internationale Patentnummer
Link zur Lizenz
Angaben zur Forschungsförderung
Projekt
Open Access-Veröffentlichung
Open Access Green
Sammlungen
Core Facility der Universität Konstanz
Titel in einer weiteren Sprache
Publikationstyp
Preprint
Publikationsstatus
Published
Erschienen in
Zusammenfassung
A positivity-preserving numerical scheme for a fourth order nonlinear parabolic system arising in quantum semiconductor modelling is studied. The system is numerically treated by introducing an additional nonlinear potential and a subsequent semidiscretization in time. The resulting sequence of nonlinear second order elliptic systems admits at each time level strictly positive solutions, which is proved by an exponential transformation of variables. The stability of the scheme is shown and convergence is proved in one space dimension. The results extend under additional assumptions to the multi-dimensional case. Assuming enough regularity on the solution the rate of convergence proves to be optimal. Numerical results concerning the switching behaviour of a resonant tunneling diode are presented.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
004 Informatik
Schlagwörter
Konferenz
Rezension
undefined / . - undefined, undefined
Zitieren
ISO 690
JÜNGEL, Ansgar, René PINNAU, 2000. A Positivity-preserving Numerical Scheme for a Nonlinear Fourth Order Parabolic SystemBibTex
@unpublished{Jungel2000Posit-6224,
year={2000},
title={A Positivity-preserving Numerical Scheme for a Nonlinear Fourth Order Parabolic System},
author={Jüngel, Ansgar and Pinnau, René}
}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/123456789/6224">
<dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
<dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/6224/1/preprint_112.pdf"/>
<dc:creator>Pinnau, René</dc:creator>
<bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/6224"/>
<dc:language>eng</dc:language>
<dc:contributor>Jüngel, Ansgar</dc:contributor>
<dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/36"/>
<dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-24T16:10:22Z</dc:date>
<dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-24T16:10:22Z</dcterms:available>
<dcterms:title>A Positivity-preserving Numerical Scheme for a Nonlinear Fourth Order Parabolic System</dcterms:title>
<dc:creator>Jüngel, Ansgar</dc:creator>
<dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/36"/>
<dcterms:abstract xml:lang="eng">A positivity-preserving numerical scheme for a fourth order nonlinear parabolic system arising in quantum semiconductor modelling is studied. The system is numerically treated by introducing an additional nonlinear potential and a subsequent semidiscretization in time. The resulting sequence of nonlinear second order elliptic systems admits at each time level strictly positive solutions, which is proved by an exponential transformation of variables. The stability of the scheme is shown and convergence is proved in one space dimension. The results extend under additional assumptions to the multi-dimensional case. Assuming enough regularity on the solution the rate of convergence proves to be optimal. Numerical results concerning the switching behaviour of a resonant tunneling diode are presented.</dcterms:abstract>
<dc:rights>terms-of-use</dc:rights>
<dc:contributor>Pinnau, René</dc:contributor>
<void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
<foaf:homepage rdf:resource="http://localhost:8080/"/>
<dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/6224/1/preprint_112.pdf"/>
<dc:format>application/pdf</dc:format>
<dcterms:issued>2000</dcterms:issued>
</rdf:Description>
</rdf:RDF>
