Show simple item record

dc.contributor.authorMarica, A.
dc.contributor.authorZuazua, E.
dc.date.accessioned2016-06-13T13:33:48Z
dc.date.available2016-06-13T13:33:48Z
dc.date.issued2014-12-31
dc.identifier.isbn978-1-4614-5811-1
dc.identifier.urihttp://hdl.handle.net/20.500.11824/225
dc.description.abstractThis work describes the propagation properties of the so-called symmetric interior penalty discontinuous Galerkin (SIPG) approximations of the 1-d wave equation. This is done by means of linear approximations on uniform meshes. First, a careful Fourier analysis is constructed, highlighting the coexistence of two Fourier spectral branches or spectral diagrams (physical and spurious) related to the two components of the numerical solution (averages and jumps). Efficient filtering mechanisms are also developed by means of techniques previously proved to be appropriate for classical schemes like finite differences or P1-classical finite elements. In particular, the work presents a proof that the uniform observability property is recovered uniformly by considering initial data with null jumps and averages given by a bi-grid filtering algorithm. Finally, the book explains how these results can be extended to other more sophisticated conforming and non-conforming finite element methods, in particular to quadratic finite elements, local discontinuous Galerkin methods and a version of the SIPG method adding penalization on the normal derivatives of the numerical solution at the grid points. This work is the first publication to contain a rigorous analysis of the discontinuous Galerkin methods for wave control problems. It will be of interest to a range of researchers specializing in wave approximations.
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.titleSymmetric discontinuous Galerkin approximations of waves: high frequency propagation and control
dc.typeinfo:eu-repo/semantics/bookParten_US
dc.identifier.doi10.1007/978-1-4614-5811-1
dc.relation.publisherversionhttp://www.springer.com/gp/book/9781461458104
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/closedAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US
dc.journal.titleBCAM Springer Briefs in Mathematicsen_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record

Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España