Please use this identifier to cite or link to this item: http://dx.doi.org/10.25673/101186
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dc.contributor.authorSoszyńska, Martyna-
dc.contributor.authorRichter, Thomas-
dc.date.accessioned2023-02-13T12:48:42Z-
dc.date.available2023-02-13T12:48:42Z-
dc.date.issued2021-
dc.date.submitted2021-
dc.identifier.urihttps://opendata.uni-halle.de//handle/1981185920/103142-
dc.identifier.urihttp://dx.doi.org/10.25673/101186-
dc.description.abstractWe study the dynamics of a parabolic and a hyperbolic equation coupled on a common interface.We develop time-stepping schemes that can use different time-step sizes for each of the subproblems. The problem is formulated in a strongly coupled (monolithic) space-time framework. Coupling two different step sizes monolithically gives rise to large algebraic systems of equations. There, multiple states of the subproblems must be solved at once. For efficiently solving these algebraic systems, we inherit ideas from the partitioned regime. Therefore we present two decoupling methods, namely a partitioned relaxation scheme and a shooting method. Furthermore, we develop an a posteriori error estimator serving as a mean for an adaptive time-stepping procedure. The goal is to optimally balance the time-step sizes of the two subproblems. The error estimator is based on the dual weighted residual method and relies on the space-time Galerkin formulation of the coupled problem. As an example, we take a linear set-up with the heat equation coupled to the wave equation. We formulate the problem in a monolithic manner using the space-time framework. In numerical test cases, we demonstrate the efficiency of the solution process and we also validate the accuracy of the a posteriori error estimator and its use for controlling the time-step sizes.eng
dc.description.sponsorshipProjekt DEAL 2021-
dc.language.isoeng-
dc.relation.ispartofhttp://link.springer.com/journal/10543-
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/-
dc.subjectMultirate time-steppingeng
dc.subjectGalerkin time discretizationeng
dc.subjectA posteriori error estimationeng
dc.subjectPartitioned solutioneng
dc.subject.ddc510.72-
dc.titleAdaptive time-step control for a monolithic multirate scheme coupling the heat and wave equationeng
dc.typeArticle-
dc.identifier.urnurn:nbn:de:gbv:ma9:1-1981185920-1031426-
local.versionTypepublishedVersion-
local.bibliographicCitation.journaltitleBIT-
local.bibliographicCitation.volume61-
local.bibliographicCitation.pagestart1367-
local.bibliographicCitation.pageend1396-
local.bibliographicCitation.publishernameSpringer Science + Business Media B.V-
local.bibliographicCitation.publisherplaceDordrecht [u.a.]-
local.bibliographicCitation.doi10.1007/s10543-021-00854-3-
local.openaccesstrue-
dc.identifier.ppn1780487746-
local.bibliographicCitation.year2021-
cbs.sru.importDate2023-02-13T12:44:27Z-
local.bibliographicCitationEnthalten in BIT - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1961-
local.accessrights.dnbfree-
Appears in Collections:Fakultät für Mathematik (OA)

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