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dc.contributor.authorErvedoza S.
dc.contributor.authorZuazua E.
dc.date.accessioned2017-02-21T08:18:17Z
dc.date.available2017-02-21T08:18:17Z
dc.date.issued2009-12-31
dc.identifier.issn0021-7824
dc.identifier.urihttp://hdl.handle.net/20.500.11824/504
dc.description.abstractWe consider time semi-discrete approximations of a class of exponentially stable infinite-dimensional systems modeling, for instance, damped vibrations. It has recently been proved that for time semi-discrete systems, due to high frequency spurious components, the exponential decay property may be lost as the time step tends to zero. We prove that adding a suitable numerical viscosity term in the numerical scheme, one obtains approximations that are uniformly exponentially stable. This result is then combined with previous ones on space semi-discretizations to derive similar results on fully-discrete approximation schemes. Our method is mainly based on a decoupling argument of low and high frequencies, the low frequency observability property for time semi-discrete approximations of conservative linear systems and the dissipativity of the numerical viscosity on the high frequency components. Our methods also allow to deal directly with stabilization properties of fully discrete approximation schemes without numerical viscosity, under a suitable CFL type condition on the time and space discretization parameters. © 2008 Elsevier Masson SAS. All rights reserved.
dc.formatapplication/pdf
dc.languageeng
dc.publisherJournal des Mathematiques Pures et Appliquees
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/
dc.subjectDamped systems
dc.subjectStabilization
dc.subjectTime semi-discretizations
dc.titleUniformly exponentially stable approximations for a class of damped systems
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion
dc.identifier.doi10.1016/j.matpur.2008.09.002
dc.relation.publisherversionhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-57849116170&doi=10.1016%2fj.matpur.2008.09.002&partnerID=40&md5=c1b83981065b63fdec3d03857d5eb908


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