Symmetric Discontinuous Galerkin Methods for 1-D Waves: Fourier Analysis, Propagation, Observability and Applications (SpringerBriefs in Mathematics) - Softcover

Buch 38 von 155: SpringerBriefs in Mathematics

Marica, Aurora

 
9781461458104: Symmetric Discontinuous Galerkin Methods for 1-D Waves: Fourier Analysis, Propagation, Observability and Applications (SpringerBriefs in Mathematics)
Softcover
ISBN 10: 1461458102 ISBN 13: 9781461458104
Verlag: Springer, 2014

Inhaltsangabe

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.

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Reseña del editor

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.

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Verlag
Springer
Erscheinungsdatum
2014
Sprache
Englisch
ISBN 10 
1461458102
ISBN 13 
9781461458104
Einband
Tapa blanda
Anzahl der Seiten
120
Kontakt zum Hersteller
Nicht verfügbar
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Weitere beliebte Ausgaben desselben Titels

9781461458128: Symmetric Discontinuous Galerkin Methods for 1-D Waves: Fourier Analysis, Propagation, Observability and Applications

Vorgestellte Ausgabe

ISBN 10:  1461458129 ISBN 13:  9781461458128
Verlag: Springer, 2014
Softcover