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dc.contributor.authorFilbet, Francis
dc.contributor.authorMouhot, Clément
HAL ID: 1892
dc.date.accessioned2010-02-16T14:32:12Z
dc.date.available2010-02-16T14:32:12Z
dc.date.issued2011
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/3475
dc.language.isoenen
dc.subjectBoltzmann equationen
dc.subjectspectral methodsen
dc.subjectnumerical stabilityen
dc.subjectasymptotic stabilityen
dc.subjectFourier-Galerkin methoden
dc.subject.ddc519en
dc.titleAnalysis of spectral methods for the homogeneous Boltzmann equationen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThe development of accurate and fast algorithms for the Boltzmann collision integral and their analysis represent a challenging problem in scientific computing and numerical analysis. Recently, several works were devoted to the derivation of spectrally accurate schemes for the Boltzmann equation, but very few of them were concerned with the stability analysis of the method. In particular there was no result of stability except when the method is modified in order to enforce the posivity preservation, which destroys the spectral accuracy. In this paper we propose a new method to study the stability of homogeneous Boltzmann equations perturbed by smoothed balanced operators which do not preserve positivity of the distribution. This method takes advantage of the ``spreading'' property of the collision, together with estimates on regularity and entropy production. As an application we prove stability and convergence of spectral methods for the Boltzmann equation, when the discretization parameter is large enough (with explicit bound).en
dc.relation.isversionofjnlnameTransactions of the American Mathematical Society
dc.relation.isversionofjnlvol363
dc.relation.isversionofjnlissue4
dc.relation.isversionofjnldate2011
dc.relation.isversionofjnlpages1947-1980
dc.relation.isversionofdoihttp://dx.doi.org/10.1090/S0002-9947-2010-05303-6
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00339426/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherAmerican Mathematical Societyen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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