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A modified perturbation method for mathematical models with randomness: An analysis through the steady-state solution to Burgers’ PDE
dc.contributor.author | Calatayud, Julia | |
dc.contributor.author | Cortés, Juan Carlos | |
dc.contributor.author | Jornet, Marc | |
dc.date.accessioned | 2021-10-19T12:58:41Z | |
dc.date.available | 2021-10-19T12:58:41Z | |
dc.date.issued | 2020-04-12 | |
dc.identifier.citation | Calatayud J, Cortés JC, Jornet M. A modified perturbation method for mathematicalmodels with randomness: An analysis through the steady-state solution to Burgers' partial differential equation.Math Meth Appl Sci. 2021;44:11820–11827. https://doi.org/10.1002/mma.6420CALATAYUD ET AL.11827 | ca_CA |
dc.identifier.issn | 0170-4214 | |
dc.identifier.issn | 1099-1476 | |
dc.identifier.uri | http://hdl.handle.net/10234/195079 | |
dc.description.abstract | The variability of the data and the incomplete knowledge of the true physics require the incorporation of randomness into the formulation of mathematical models. In this setting, the deterministic numerical methods cannot capture the propagation of the uncertainty from the inputs to the model output. For some problems, such as the Burgers' equation (simplification to understand properties of the Navier–Stokes equations), a small variation in the parameters causes nonnegligible changes in the output. Thus, suitable techniques for uncertainty quantification must be used. The generalized polynomial chaos (gPC) method has been successfully applied to compute the location of the transition layer of the steady-state solution, when a small uncertainty is incorporated into the boundary. On the contrary, the classical perturbation method does not give reliable results, due to the uncertainty magnitude of the output. We propose a modification of the perturbation method that converges and is comparable with the gPC approach in terms of efficiency and rate of convergence. The method is even applicable when the input random parameters are dependent random variables. | ca_CA |
dc.format.extent | 8 p. | ca_CA |
dc.format.mimetype | application/pdf | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | John Wiley and Sons | ca_CA |
dc.publisher | Wiley | ca_CA |
dc.relation.isPartOf | Math Meth Appl Sci. 2021;44:11820–11827 | ca_CA |
dc.relation.uri | https://onlinelibrary.wiley.com/action/downloadFigures?id=mma6420-fig-0001&doi=10.1002%2Fmma.6420 | ca_CA |
dc.rights | © 2020 John Wiley & Sons, Ltd. | ca_CA |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | ca_CA |
dc.subject | Burgers' equation | ca_CA |
dc.subject | gPC expansion | ca_CA |
dc.subject | Navier–Stokes equation | ca_CA |
dc.subject | perturbation method | ca_CA |
dc.subject | randomnessanalysis | ca_CA |
dc.title | A modified perturbation method for mathematical models with randomness: An analysis through the steady-state solution to Burgers’ PDE | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | https://doi.org/10.1002/mma.6420 | |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca_CA |
dc.relation.publisherVersion | https://onlinelibrary.wiley.com/journal/10991476 | ca_CA |
dc.type.version | info:eu-repo/semantics/acceptedVersion | ca_CA |
project.funder.name | Ministerio de Economía y Competitividad | ca_CA |
project.funder.name | Agencia Estatal de Investigación (AEI) | ca_CA |
project.funder.name | Fondo Europeo de Desarrollo Regional (FEDER UE) | ca_CA |
oaire.awardNumber | MTM2017-89664-P | ca_CA |
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