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)
Resource Information
The item Symmetric discontinuous Galerkin approximations of 1-D waves : Fourier analysis, propagation, observability and applications, by Aurora Marica, Enrique Zuazua, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Symmetric discontinuous Galerkin approximations of 1-D waves : Fourier analysis, propagation, observability and applications, by Aurora Marica, Enrique Zuazua, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
- 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
- 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. 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
- Isbn
- 9781461458104
- 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
- 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
- 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)
- 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)
- 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
Library Links
Embed
Settings
Select options that apply then copy and paste the RDF/HTML data fragment to include in your application
Embed this data in a secure (HTTPS) page:
Layout options:
Include data citation:
<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Symmetric-discontinuous-Galerkin-approximations/8V1G0gJe7pY/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/Symmetric-discontinuous-Galerkin-approximations/8V1G0gJe7pY/">Symmetric discontinuous Galerkin approximations of 1-D waves : Fourier analysis, propagation, observability and applications, by Aurora Marica, Enrique Zuazua, (electronic book)</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>
Note: Adjust the width and height settings defined in the RDF/HTML code fragment to best match your requirements
Preview
Cite Data - Experimental
Data Citation of the Item Symmetric discontinuous Galerkin approximations of 1-D waves : Fourier analysis, propagation, observability and applications, by Aurora Marica, Enrique Zuazua, (electronic book)
Copy and paste the following RDF/HTML data fragment to cite this resource
<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Symmetric-discontinuous-Galerkin-approximations/8V1G0gJe7pY/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/Symmetric-discontinuous-Galerkin-approximations/8V1G0gJe7pY/">Symmetric discontinuous Galerkin approximations of 1-D waves : Fourier analysis, propagation, observability and applications, by Aurora Marica, Enrique Zuazua, (electronic book)</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>
