POD Galerkin schemes for nonlinear elliptic-parabolic systems

Lass, Oliver; Volkwein, Stefan

POD Galerkin schemes for nonlinear elliptic-parabolic systems

Files

EllipticParabolicPOD.pdf(1.12 MB)

Date

2012

Authors

Lass, Oliver

Volkwein, Stefan

Series

Konstanzer Schriften in Mathematik; 301

Publication type

Preprint

Abstract

In this paper the authors study a nonlinear elliptic-parabolic system, which is motivated by mathematical models for lithium ion batteries. For the reliable and fast numerical solution of the system a reduced-order approach based on proper orthogonal decomposition (POD) is applied. The strategy is justified by an a-priori error estimate for the error between the solution to the coupled system and its POD approximation. The nonlinear coupling is realized by variants of the empirical interpolation introduced by Barrault et al. and Chaturantabut et al. Numerical examples illustrate the efficiency of the proposed reduced-order modeling.

Subject (DDC)

510 Mathematics

Keywords

Elliptic parabolic systems,semilinear equations,newton method,proper orthogonal decomposition,empirical interpolation,error estimates

Cite This

ISO 690

LASS, Oliver, Stefan VOLKWEIN, 2012. POD Galerkin schemes for nonlinear elliptic-parabolic systems

BibTex

@unpublished{Lass2012Galer-18468,
  year={2012},
  title={POD Galerkin schemes for nonlinear elliptic-parabolic systems},
  author={Lass, Oliver 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/123456789/18468">
    <dc:creator>Lass, Oliver</dc:creator>
    <dcterms:abstract xml:lang="eng">In this paper the authors study a nonlinear elliptic-parabolic system, which is motivated by mathematical models for lithium ion batteries. For the reliable and fast numerical solution of the system a reduced-order approach based on proper orthogonal decomposition (POD) is applied. The strategy is justified by an a-priori error estimate for the error between the solution to the coupled system and its POD approximation. The nonlinear coupling is realized by variants of the empirical interpolation introduced by Barrault et al. and Chaturantabut et al. Numerical examples illustrate the efficiency of the proposed reduced-order modeling.</dcterms:abstract>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:contributor>Lass, Oliver</dc:contributor>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dcterms:title>POD Galerkin schemes for nonlinear elliptic-parabolic systems</dcterms:title>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2012-03-05T11:10:38Z</dcterms:available>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2012-03-05T11:10:38Z</dc:date>
    <dc:creator>Volkwein, Stefan</dc:creator>
    <dc:rights>terms-of-use</dc:rights>
    <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/18468"/>
    <dc:contributor>Volkwein, Stefan</dc:contributor>
    <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/18468/2/EllipticParabolicPOD.pdf"/>
    <dcterms:issued>2012</dcterms:issued>
    <dc:language>eng</dc:language>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/18468/2/EllipticParabolicPOD.pdf"/>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
  </rdf:Description>
</rdf:RDF>

Bibliography of Konstanz

Yes