01561nam 2200361 450 991069108590332120130926111212.0(CKB)5470000002343491(OCoLC)858943037(EXLCZ)99547000000234349120130926d1996 ua 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierAn Act to Amend the Foreign Assistance Act of 1961 and the Arms Export Control Act to Make Improvements to Certain Defense and Security Assistance Provisions under those Acts, to Authorize the Transfer of Naval Vessels to Certain Foreign Countries, and for Other Purposes[Washington, D.C.] :[U.S. Government Printing Office],[1996]1online resource (22 unnumbered pages)Title from title screen (viewed on September 26, 2013)."July 21, 1996, (H.R. 3121).""110 Stat. 1421.""Public Law 104-164."WarshipsMilitary assistance, AmericanWarships.Military assistance, American.GPOGPOBOOK9910691085903321An Act to Amend the Foreign Assistance Act of 1961 and the Arms Export Control Act to Make Improvements to Certain Defense and Security Assistance Provisions under those Acts, to Authorize the Transfer of Naval Vessels to Certain Foreign Countries, and for Other Purposes3487743UNINA05011nam 22008295 450 991029997710332120251117074534.01-4614-5811-010.1007/978-1-4614-5811-1(CKB)3710000000093418(SSID)ssj0001187553(PQKBManifestationID)11673376(PQKBTitleCode)TC0001187553(PQKBWorkID)11258055(PQKB)11276801(MiAaPQ)EBC1698429(DE-He213)978-1-4614-5811-1(PPN)17782302X(EXLCZ)99371000000009341820140310d2014 u| 0engurcnu||||||||txtccrSymmetric Discontinuous Galerkin Methods for 1-D Waves Fourier Analysis, Propagation, Observability and Applications /by Aurora Marica, Enrique Zuazua1st ed. 2014.New York, NY :Springer New York :Imprint: Springer,2014.1 online resource (114 pages) illustrations (some color)SpringerBriefs in Mathematics,2191-8198Bibliographic Level Mode of Issuance: Monograph1-4614-5810-2 Includes bibliographical references.1. Preliminaries -- 2. Discontinuous Galerkin approximations and main results -- 3. Bibliographical notes -- 4. Fourier analysis of the DG methods -- 5. Non-uniform observability for DG approximations of waves -- 6. Filtering mechanisms -- 7. Extensions to other numerical approximation schemes -- 8. Comments and open problems -- A technical proof -- References.This 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.SpringerBriefs in Mathematics,2191-8198Numerical analysisFourier analysisApproximation theoryDifferential equations, PartialAlgorithmsApplied mathematicsEngineering mathematicsNumerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M14050Fourier Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12058Approximations and Expansionshttps://scigraph.springernature.com/ontologies/product-market-codes/M12023Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Algorithmshttps://scigraph.springernature.com/ontologies/product-market-codes/M14018Applications of Mathematicshttps://scigraph.springernature.com/ontologies/product-market-codes/M13003Numerical analysis.Fourier analysis.Approximation theory.Differential equations, Partial.Algorithms.Applied mathematics.Engineering mathematics.Numerical Analysis.Fourier Analysis.Approximations and Expansions.Partial Differential Equations.Algorithms.Applications of Mathematics.530.124Marica Auroraauthttp://id.loc.gov/vocabulary/relators/aut721756Zuazua E(Enrique),authttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910299977103321Symmetric Discontinuous Galerkin Methods for 1-D Waves2512150UNINA