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The Resource Symmetric discontinuous Galerkin approximations of 1-D waves : Fourier analysis, propagation, observability and applications, by Aurora Marica, Enrique Zuazua, (electronic book)

Symmetric discontinuous Galerkin approximations of 1-D waves : Fourier analysis, propagation, observability and applications, by Aurora Marica, Enrique Zuazua, (electronic book)

Label
Symmetric discontinuous Galerkin approximations of 1-D waves : Fourier analysis, propagation, observability and applications
Title
Symmetric discontinuous Galerkin approximations of 1-D waves
Title remainder
Fourier analysis, propagation, observability and applications
Statement of responsibility
by Aurora Marica, Enrique Zuazua
Creator
Contributor
Author
Subject
Language
eng
Summary
This workdescribes 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, 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 P1-classical 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 bi-grid filtering algorithm. Finally, the bookexplains how theseresults can be extended to other more sophisticated conforming and non-conforming 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
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Marica, Aurora
Dewey number
530.124
Illustrations
illustrations
Index
no index present
LC call number
QC157
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Zuazua, E.
Series statement
SpringerBriefs in mathematics
http://library.link/vocab/subjectName
  • Waves
  • Galerkin methods
  • Approximation theory
Label
Symmetric discontinuous Galerkin approximations of 1-D waves : Fourier analysis, propagation, observability and applications, by Aurora Marica, Enrique Zuazua, (electronic book)
Instantiates
Publication
Antecedent source
unknown
Color
multicolored
Contents
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
Control code
SPR874021860
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9781461458104
Level of compression
unknown
Other control number
10.1007/978-1-4614-5811-1
Quality assurance targets
not applicable
Reformatting quality
unknown
Reproduction note
Electronic resource.
Sound
unknown sound
Specific material designation
remote
Label
Symmetric discontinuous Galerkin approximations of 1-D waves : Fourier analysis, propagation, observability and applications, by Aurora Marica, Enrique Zuazua, (electronic book)
Publication
Antecedent source
unknown
Color
multicolored
Contents
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
Control code
SPR874021860
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9781461458104
Level of compression
unknown
Other control number
10.1007/978-1-4614-5811-1
Quality assurance targets
not applicable
Reformatting quality
unknown
Reproduction note
Electronic resource.
Sound
unknown sound
Specific material designation
remote

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