dc.contributor.author
Hakula, Harri
dc.contributor.author
Harbrecht, Helmut
dc.contributor.author
Kaarnioja, Vesa
dc.contributor.author
Kuo, Frances Y.
dc.contributor.author
Sloan, Ian H.
dc.date.accessioned
2024-02-06T14:25:40Z
dc.date.available
2024-02-06T14:25:40Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/42245
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-41971
dc.description.abstract
We consider uncertainty quantification for the Poisson problem subject to domain uncertainty. For the stochastic parameterization of the random domain, we use the model recently introduced by Kaarnioja et al. (SIAM J. Numer. Anal., 2020) in which a countably infinite number of independent random variables enter the random field as periodic functions. We develop lattice quasi-Monte Carlo (QMC) cubature rules for computing the expected value of the solution to the Poisson problem subject to domain uncertainty. These QMC rules can be shown to exhibit higher order cubature convergence rates permitted by the periodic setting independently of the stochastic dimension of the problem. In addition, we present a complete error analysis for the problem by taking into account the approximation errors incurred by truncating the input random field to a finite number of terms and discretizing the spatial domain using finite elements. The paper concludes with numerical experiments demonstrating the theoretical error estimates.
en
dc.format.extent
45 Seiten
dc.rights.uri
https://creativecommons.org/licenses/by/4.0/
dc.subject
uncertainty quantification
en
dc.subject
random domains
en
dc.subject
periodic random variables
en
dc.subject.ddc
500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik
dc.title
Uncertainty quantification for random domains using periodic random variables
dc.type
Wissenschaftlicher Artikel
dcterms.bibliographicCitation.doi
10.1007/s00211-023-01392-6
dcterms.bibliographicCitation.journaltitle
Numerische Mathematik
dcterms.bibliographicCitation.number
1
dcterms.bibliographicCitation.pagestart
273
dcterms.bibliographicCitation.pageend
317
dcterms.bibliographicCitation.volume
156
dcterms.bibliographicCitation.url
https://doi.org/10.1007/s00211-023-01392-6
refubium.affiliation
Mathematik und Informatik
refubium.affiliation.other
Institut für Mathematik
refubium.funding
Springer Nature DEAL
refubium.note.author
Die Publikation wurde aus Open Access Publikationsgeldern der Freien Universität Berlin gefördert.
refubium.resourceType.isindependentpub
no
dcterms.accessRights.openaire
open access
dcterms.isPartOf.eissn
0945-3245