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Symmetric Discontinuous Galerkin Methods for 1-D Waves: Fourier Analysis, Propagation, Observability and Applications (SpringerBriefs in Mathematics) - Softcover
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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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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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Symmetric Discontinuous Galerkin Methods for 1-D Waves: Fourier Analysis, Propagation, Observability and Applications (SpringerBriefs in Mathematics)
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Symmetric Discontinuous Galerkin Methods for 1-D Waves
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Springer New York, Springer US Mär 2014, 2014
ISBN 10: 1461458102
ISBN 13: 9781461458104
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Taschenbuch. Zustand: Neu. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 120 pp. Englisch. Bestandsnummer des Verkäufers 9781461458104
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Symmetric Discontinuous Galerkin Methods for 1-D Waves
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Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 120 pp. Englisch. Bestandsnummer des Verkäufers 9781461458104
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Symmetric Discontinuous Galerkin Methods for 1-D Waves: Fourier Analysis, Propagation, Observability and Applications (SpringerBriefs in Mathematics)
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Symmetric Discontinuous Galerkin Methods for 1-D Waves : Fourier Analysis, Propagation, Observability and Applications
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Springer New York, Springer New York, 2014
ISBN 10: 1461458102
ISBN 13: 9781461458104
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Bestandsnummer des Verkäufers 9781461458104
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Symmetric Discontinuous Galerkin Methods for 1-D Waves: Fourier Analysis, Propagation, Observability and Applications (SpringerBriefs in Mathematics)
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Symmetric Discontinuous Galerkin Methods for 1-D Waves : Fourier Analysis, Propagation, Observability and Applications
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Symmetric Discontinuous Galerkin Methods for 1-D Waves: Fourier Analysis, Propagation, Observability and Applications
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