Symmetric discontinuous Galerkin methods of 1D waves : Fourier analysis, propagation, observability and applications
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The work Symmetric discontinuous Galerkin methods of 1D waves : Fourier analysis, propagation, observability and applications represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.
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Symmetric discontinuous Galerkin methods of 1D waves : Fourier analysis, propagation, observability and applications
Resource Information
The work Symmetric discontinuous Galerkin methods of 1D waves : Fourier analysis, propagation, observability and applications represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Symmetric discontinuous Galerkin methods of 1D waves : Fourier analysis, propagation, observability and applications
 Title remainder
 Fourier analysis, propagation, observability and applications
 Statement of responsibility
 by Aurora Marica, Enrique Zuazua
 Language
 eng
 Summary
 This workdescribes the propagation properties of the socalled symmetric interior penalty discontinuous Galerkin (SIPG) approximations of the 1d wave equation. This is done by means of linear approximations on uniform meshes. First, a careful Fourier analysis is constructed, highlightingthe 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 developedby means of techniques previously proved to be appropriate for classical schemes like finite differences or P1classical finite elements. In particular, the work presents a proof thatthe uniform observability property is recovered uniformly by considering initial data with null jumps and averages given by a bigrid filtering algorithm. Finally, the bookexplains how theseresults can be extended to other more sophisticated conforming and nonconforming finite element methods, in particular to quadratic finiteelements, 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 tocontaina rigorous analysis of the discontinuous Galerkin methods for wave control problems. It will be of interest to a range of researchers specializing inwave approximations
 Cataloging source
 GW5XE
 Dewey number
 530.124
 Illustrations
 illustrations
 Index
 no index present
 LC call number
 QC157
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 SpringerBriefs in mathematics
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