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dc.contributor.authorLanger, Ulrich
dc.contributor.authorMatculevich, Svetlana
dc.contributor.authorRepin, Sergey
dc.date.accessioned2019-09-25T07:22:58Z
dc.date.available2021-10-17T21:35:09Z
dc.date.issued2019fi
dc.identifier.citationLanger, U., Matculevich, S., & Repin, S. (2019). Guaranteed error bounds and local indicators for adaptive solvers using stabilised space-time IgA approximations to parabolic problems. <em>Computers and Mathematics with Applications</em>, 78 (8), 2641-2671. <a href="https://doi.org/10.1016/j.camwa.2019.04.009">doi:10.1016/j.camwa.2019.04.009</a>fi
dc.identifier.otherTUTKAID_81621
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/65640
dc.description.abstractThe paper is concerned with space–time IgA approximations to parabolic initial–boundary value problems. We deduce guaranteed and fully computable error bounds adapted to special features of such type of approximations and investigate their efficiency. The derivation of error estimates is based on the analysis of the corresponding integral identity and exploits purely functional arguments in the maximal parabolic regularity setting. The estimates are valid for any approximation from the admissible (energy) class and do not contain mesh-dependent constants. They provide computable and fully guaranteed error bounds for the norms arising in stabilised space–time approximations. Furthermore, a posterior error estimates yield efficient error indicators enhancing the performance of adaptive solvers and generate very successful mesh refinement procedures. Theoretical results are verified with a series of numerical examples, in which approximate solutions and the corresponding fluxes are recovered by IgA techniques. The numerical results confirm the high efficiency of the method in the context of the two main goals of a posteriori error analysis: estimation of global errors and mesh adaptation.fi
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherElsevier
dc.relation.ispartofseriesComputers and Mathematics with Applications
dc.rightsIn Copyright
dc.subject.othernumeerinen analyysifi
dc.subject.otherosittaisdifferentiaaliyhtälötfi
dc.subject.otherominaisarvotfi
dc.subject.othervirheanalyysifi
dc.subject.otherfunctional error estimatesfi
dc.subject.otherstabilised space–time IgA schemesfi
dc.subject.otherparabolic initial-value boundary problemsfi
dc.subject.otherguaranteed error boundsfi
dc.subject.otheradaptive space–time schemesfi
dc.titleGuaranteed error bounds and local indicators for adaptive solvers using stabilised space-time IgA approximations to parabolic problemsfi
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201909114108
dc.contributor.laitosInformaatioteknologian tiedekuntafi
dc.contributor.laitosFaculty of Information Technologyen
dc.contributor.oppiaineTietotekniikka
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.date.updated2019-09-11T09:15:38Z
dc.description.reviewstatuspeerReviewed
dc.format.pagerange2641-2671
dc.relation.issn0898-1221
dc.relation.numberinseries8
dc.relation.volume78
dc.type.versionacceptedVersion
dc.rights.copyright© 2019 Elsevier Ltd
dc.rights.accesslevelopenAccessfi
dc.format.contentfulltext
dc.rights.urlhttp://rightsstatements.org/page/InC/1.0/?language=en
dc.relation.doi10.1016/j.camwa.2019.04.009


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