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dc.contributor.authorAntonopoulou, Dimitra
dc.contributor.authorBanas, Lubomir
dc.contributor.authorNurnberg, Robert
dc.contributor.authorProhl, Andreas
dc.date.accessioned2021-01-28T10:39:22Z
dc.date.available2021-01-28T10:39:22Z
dc.identifierhttps://chesterrep.openrepository.com/bitstream/handle/10034/624203/NMAntonopoulou1905.11050.pdf?sequence=1
dc.identifier.citationAntonopoulou, D., Banas, L., Nurnberg, R. & Prohl, A. (2021). Numerical approximation of the Stochastic Cahn-Hilliard Equation near the Sharp Interface Limit. Numerische Mathematik, 147, 505-551. https://doi.org/10.1007/s00211-021-01179-7en_US
dc.identifier.issn0029-599X
dc.identifier.doi10.1007/s00211-021-01179-7
dc.identifier.urihttp://hdl.handle.net/10034/624203
dc.description.abstractAbstract. We consider the stochastic Cahn-Hilliard equation with additive noise term that scales with the interfacial width parameter ε. We verify strong error estimates for a gradient flow structure-inheriting time-implicit discretization, where ε only enters polynomially; the proof is based on higher-moment estimates for iterates, and a (discrete) spectral estimate for its deterministic counterpart. For γ sufficiently large, convergence in probability of iterates towards the deterministic Hele-Shaw/Mullins-Sekerka problem in the sharp-interface limit ε → 0 is shown. These convergence results are partly generalized to a fully discrete finite element based discretization. We complement the theoretical results by computational studies to provide practical evidence concerning the effect of noise (depending on its ’strength’ γ) on the geometric evolution in the sharp-interface limit. For this purpose we compare the simulations with those from a fully discrete finite element numerical scheme for the (stochastic) Mullins-Sekerka problem. The computational results indicate that the limit for γ ≥ 1 is the deterministic problem, and for γ = 0 we obtain agreement with a (new) stochastic version of the Mullins-Sekerka problem.en_US
dc.publisherSpringeren_US
dc.relation.urlhttps://link.springer.com/article/10.1007/s00211-021-01179-7en_US
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/en_US
dc.titleNumerical approximation of the Stochastic Cahn-Hilliard Equation near the Sharp Interface Limiten_US
dc.typeArticleen_US
dc.identifier.eissn0945-3245en_US
dc.contributor.departmentUniversity of Chester; University of Bielefeld; Imperial College London; University of Tuebingenen_US
dc.identifier.journalNumerische Mathematiken_US
or.grant.openaccessYesen_US
rioxxterms.funderUnfundeden_US
rioxxterms.identifier.projectUnfundeden_US
rioxxterms.versionAMen_US
rioxxterms.licenseref.startdate2022-02-17
dcterms.dateAccepted2020-12-24
rioxxterms.publicationdate2021-02-17
dc.date.deposited2021-01-28en_US
dc.indentifier.issn0029-599Xen_US


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