The Resource Symmetric discontinuous Galerkin methods of 1D waves : Fourier analysis, propagation, observability and applications, by Aurora Marica, Enrique Zuazua
Symmetric discontinuous Galerkin methods of 1D waves : Fourier analysis, propagation, observability and applications, by Aurora Marica, Enrique Zuazua
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The item Symmetric discontinuous Galerkin methods of 1D waves : Fourier analysis, propagation, observability and applications, by Aurora Marica, Enrique Zuazua represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Symmetric discontinuous Galerkin methods of 1D waves : Fourier analysis, propagation, observability and applications, by Aurora Marica, Enrique Zuazua represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 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
 Language
 eng
 Extent
 1 online resource.
 Contents

 1. Preliminaries
 2. Discontinuous Galerkin approximations and main results
 3. Bibliographical notes
 4. Fourier analysis of the DG methods
 5. Nonuniform 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
 Isbn
 9781461458111
 Label
 Symmetric discontinuous Galerkin methods of 1D waves : Fourier analysis, propagation, observability and applications
 Title
 Symmetric discontinuous Galerkin methods of 1D waves
 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
 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
 SCIENCE
 SCIENCE
 SCIENCE
 Approximation theory
 Galerkin methods
 Waves
 Label
 Symmetric discontinuous Galerkin methods of 1D waves : Fourier analysis, propagation, observability and applications, by Aurora Marica, Enrique Zuazua
 Antecedent source
 unknown
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 1. Preliminaries  2. Discontinuous Galerkin approximations and main results  3. Bibliographical notes  4. Fourier analysis of the DG methods  5. Nonuniform 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
 874021860
 Dimensions
 unknown
 Extent
 1 online resource.
 File format
 unknown
 Form of item
 online
 Isbn
 9781461458111
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9781461458111
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)874021860
 Label
 Symmetric discontinuous Galerkin methods of 1D waves : Fourier analysis, propagation, observability and applications, by Aurora Marica, Enrique Zuazua
 Antecedent source
 unknown
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 1. Preliminaries  2. Discontinuous Galerkin approximations and main results  3. Bibliographical notes  4. Fourier analysis of the DG methods  5. Nonuniform 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
 874021860
 Dimensions
 unknown
 Extent
 1 online resource.
 File format
 unknown
 Form of item
 online
 Isbn
 9781461458111
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9781461458111
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)874021860
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