Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.109
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dc.contributor.authorMedviďová-Lukáčová, Mária-
dc.contributor.authorTeschke, Ulf-
dc.date.accessioned2006-02-09T11:57:09Zde_DE
dc.date.available2006-02-09T11:57:09Zde_DE
dc.date.issued2005-03-
dc.identifier.citationPreprint. Published in: Z. angew. Math. Mech. (ZAMM), 86(11), 2006, 874–891de_DE
dc.identifier.urihttp://tubdok.tub.tuhh.de/handle/11420/111-
dc.description.abstractWe present a comparison of two discretization methods for the shallow water equations, namely the finite volume method and the finite element scheme. A reliable model for practical interests includes terms modelling the bottom topography as well as the friction effects. The resulting equations belong to the class of systems of hyperbolic partial differential equations of first order with zero order source terms, the so-called balance laws. In order to approximate correctly steady equilibrium states we need to derive a well-balanced approximation of the source term in the finite volume framework. As a result our finite volume method, a genuinely multidimensional finite volume evolution Galerkin (FVEG) scheme, approximates correctly steady states as well as their small perturbations (quasi-steady states). The second discretization scheme, which has been used for practical river flow simulations, is the finite element method (FEM). In contrary to the FVEG scheme, which is a time explicit scheme, the FEM uses an implicite time discretization and the Newton-Raphson iterative scheme for inner iterations. We compare the accuracy and performance of both scheme through several numerical experiments, which demonstrate the reliability of both discretization techniques and correct approximation of quasisteady states with bottom topography and friction.en
dc.language.isoende_DE
dc.relation.ispartofseriesPreprints des Institutes für Mathematik; Bericht 87-
dc.rightsinfo:eu-repo/semantics/openAccess-
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectwell-balanced schemes, steady states, systems of hyperbolic balance laws, shallow water equations, evolution Galerkin schemesde_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleComparison study of some finite volume and finite element methods for the shallow water equations with bottom topography and friction termsde_DE
dc.typePreprintde_DE
dc.date.updated2006-02-14T11:48:28Zde_DE
dc.identifier.urnurn:nbn:de:gbv:830-opus-1672de_DE
dc.identifier.doi10.15480/882.109-
dc.type.dinipreprint-
dc.subject.gndErhaltungssatzde
dc.subject.gndEvolutionsoperatorde
dc.subject.gndGalerkin-Methodede
dc.subject.ddccode510-
dc.subject.msc65M06:Finite difference methodsen
dc.subject.msc65L05:Initial value problemsen
dc.subject.msccode65M06-
dc.subject.msccode65L05-
dcterms.DCMITypeText-
tuhh.identifier.urnurn:nbn:de:gbv:830-opus-1672de_DE
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dc.identifier.hdl11420/111-
tuhh.abstract.englishWe present a comparison of two discretization methods for the shallow water equations, namely the finite volume method and the finite element scheme. A reliable model for practical interests includes terms modelling the bottom topography as well as the friction effects. The resulting equations belong to the class of systems of hyperbolic partial differential equations of first order with zero order source terms, the so-called balance laws. In order to approximate correctly steady equilibrium states we need to derive a well-balanced approximation of the source term in the finite volume framework. As a result our finite volume method, a genuinely multidimensional finite volume evolution Galerkin (FVEG) scheme, approximates correctly steady states as well as their small perturbations (quasi-steady states). The second discretization scheme, which has been used for practical river flow simulations, is the finite element method (FEM). In contrary to the FVEG scheme, which is a time explicit scheme, the FEM uses an implicite time discretization and the Newton-Raphson iterative scheme for inner iterations. We compare the accuracy and performance of both scheme through several numerical experiments, which demonstrate the reliability of both discretization techniques and correct approximation of quasisteady states with bottom topography and friction.de_DE
tuhh.publisher.doi10.1002/zamm.200510280-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.identifier.doi10.15480/882.109-
tuhh.type.opusPreprint (Vorabdruck)-
tuhh.institute.germanMathematik E-10de
tuhh.institute.englishMathematics E-10en
tuhh.institute.id47de_DE
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tuhh.series.namePreprints des Institutes für Mathematik-
dc.type.driverpreprint-
dc.identifier.oclc930768063-
dc.type.casraiOther-
tuhh.relation.ispartofseriesPreprints des Institutes für Mathematikde_DE
tuhh.relation.ispartofseriesnumber87de_DE
dc.identifier.scopus2-s2.0-33751394374-
datacite.resourceTypeOther-
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item.grantfulltextopen-
item.openairecristypehttp://purl.org/coar/resource_type/c_816b-
item.creatorGNDMedviďová-Lukáčová, Mária-
item.creatorGNDTeschke, Ulf-
item.openairetypePreprint-
item.tuhhseriesidPreprints des Institutes für Mathematik-
item.fulltextWith Fulltext-
item.cerifentitytypePublications-
item.creatorOrcidMedviďová-Lukáčová, Mária-
item.creatorOrcidTeschke, Ulf-
item.languageiso639-1en-
item.seriesrefPreprints des Institutes für Mathematik;87-
item.mappedtypePreprint-
crisitem.author.deptMathematik E-10-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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