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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.issued2019
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. <i>Computers and Mathematics with Applications</i>, <i>78</i>(8), 2641-2671. <a href="https://doi.org/10.1016/j.camwa.2019.04.009" target="_blank">https://doi.org/10.1016/j.camwa.2019.04.009</a>
dc.identifier.otherCONVID_30887731
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.otherfunctional error estimates
dc.subject.otherstabilised space–time IgA schemes
dc.subject.otherparabolic initial-value boundary problems
dc.subject.otherguaranteed error bounds
dc.subject.otheradaptive space–time schemes
dc.titleGuaranteed error bounds and local indicators for adaptive solvers using stabilised space-time IgA approximations to parabolic problems
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201909114108
dc.contributor.laitosInformaatioteknologian tiedekuntafi
dc.contributor.laitosFaculty of Information Technologyen
dc.contributor.oppiaineTietotekniikkafi
dc.contributor.oppiaineMathematical Information Technologyen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.date.updated2019-09-11T09:15:38Z
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
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.subject.ysovirheanalyysi
dc.subject.ysoosittaisdifferentiaaliyhtälöt
dc.subject.ysonumeerinen analyysi
dc.subject.ysoominaisarvot
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p9865
jyx.subject.urihttp://www.yso.fi/onto/yso/p12392
jyx.subject.urihttp://www.yso.fi/onto/yso/p15833
jyx.subject.urihttp://www.yso.fi/onto/yso/p7087
dc.rights.urlhttp://rightsstatements.org/page/InC/1.0/?language=en
dc.relation.doi10.1016/j.camwa.2019.04.009
jyx.fundinginformationThe research is supported by the Austrian Science Fund (FWF) through the NFN S117-03 project. This support is gratefully acknowledged. Furthermore, we appreciate the technical support and advises from Dr. Angelos Mantzaflaris, the main coordinator and developer of the open-source C++ library G+Smo that was used in our implementation and numerical tests. Last but not least, the authors would like to express their thanks to the anonymous referees for their helpful hints and valuable suggestions.
dc.type.okmA1


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