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dc.contributor.authorFeireisl, Eduard
dc.contributor.authorLukáčova-Medviďová, Mariá
dc.contributor.authorShe, Bangwei
dc.contributor.authorYuan, Yuhuan
dc.date.accessioned2022-08-25T12:58:45Z
dc.date.available2022-08-25T12:58:45Z
dc.date.issued2022-08-25
dc.identifier.urihttp://publications.mfo.de/handle/mfo/3970
dc.description.abstractThe goal of this paper is to study convergence and error estimates of the Monte Carlo method for the Navier-Stokes equations with random data. To discretize in space and time, the Monte Carlo method is combined with a suitable deterministic discretization scheme, such as a fnite volume method. We assume that the initial data, force and the viscosity coefficients are random variables and study both, the statistical convergence rates as well as the approximation errors. Since the compressible Navier-Stokes equations are not known to be uniquely solvable in the class of global weak solutions, we cannot apply pathwise arguments to analyze the random Navier-Stokes equations. Instead we have to apply intrinsic stochastic compactness arguments via the Skorokhod representation theorem and the Gyöngy-Krylov method. Assuming that the numerical solutions are bounded in probability, we prove that the Monte Carlo fnite volume method converges to a statistical strong solution. The convergence rates are discussed as well. Numerical experiments illustrate theoretical results.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2022-15
dc.subjectUncertainty quantificationen_US
dc.subjectRandom viscous compressible flowsen_US
dc.subjectStatistical solutionsen_US
dc.subjectMonte Carlo methoden_US
dc.subjectFinite volume methoden_US
dc.subjectDeterministic and statistical convergence ratesen_US
dc.titleConvergence and Error Analysis of Compressible Fluid Flows with Random Data: Monte Carlo Methoden_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2022-15
local.scientificprogramOWRF 2022en_US
local.series.idOWP-2022-15en_US
dc.identifier.urnurn:nbn:de:101:1-2022112209060989980096
dc.identifier.ppn182317910X


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