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dc.contributor.authorMarica, A.
dc.contributor.authorZuazua, E.
dc.date.accessioned2016-06-13T13:33:49Z
dc.date.available2016-06-13T13:33:49Z
dc.date.issued2014-12-31
dc.identifier.issn1439-7358
dc.identifier.urihttp://hdl.handle.net/20.500.11824/233
dc.description.abstractIn this paper, we consider the boundary stabilization problem associated to the 1- d wave equation with both variable density and diffusion coefficients and to its finite difference semi-discretizations. It is well-known that, for the finite difference semi-discretization of the constant coefficients wave equation on uniform meshes (Tébou and Zuazua, Adv. Comput. Math. 26:337–365, 2007) or on somenon-uniform meshes (Marica and Zuazua, BCAM, 2013, preprint), the discrete decay rate fails to be uniform with respect to the mesh-size parameter. We prove that, under suitable regularity assumptions on the coefficients and after adding an appropriate artificial viscosity to the numerical scheme, the decay rate is uniform as the mesh-size tends to zero. This extends previous results in Tébou and Zuazua (Adv. Comput.Math. 26:337–365, 2007) on the constant coefficient wave equation. The methodology of proof consists in applying the classical multiplier technique at the discrete level, with a multiplier adapted to the variable coefficients.
dc.formatapplication/pdf
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectDecay (organic)
dc.subjectDiffusion
dc.subjectStabilization
dc.subjectViscosity
dc.subjectArtificial viscosity
dc.subjectBoundary stabilization
dc.subjectConstant-coefficient wave equations
dc.subjectFinite difference semi-discretization
dc.subjectMultiplier techniques
dc.subjectNumerical approximations
dc.subjectRegularity assumption
dc.subjectVariable density
dc.subjectWave equations
dc.titleBoundary stabilization of numerical approximations of the 1-D variable coefficients wave equation: A numerical viscosity approach
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.1007/978-3-319-08025-3__9
dc.relation.publisherversionhttp://link.springer.com/chapter/10.1007%2F978-3-319-08025-3_9
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/FP7/246775en_US
dc.relation.projectIDES/6PN/MTM2011-29306-C02-01en_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US
dc.journal.titleLecture Notes in Computational Science and Engineeringen_US


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