Notice bibliographique

Notice

Type(s) de contenu et mode(s) de consultation : Texte noté : électronique

Auteur(s) : Marica, Aurora Voir les notices liées en tant qu'auteur
Zuazua, Enrique Voir les notices liées en tant qu'auteur

Titre(s) : Symmetric Discontinuous Galerkin Methods for 1-D Waves [Texte électronique] : Fourier Analysis, Propagation, Observability and Applications / by Aurora Marica, Enrique Zuazua

Publication : New York, NY : Springer New York : Springer e-books : Imprint: Springer, 2014

Description matérielle : 1 online resource

Collection : SpringerBriefs in Mathematics

Note(s) : 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

Sujet(s) : Mathématiques Voir les notices liées en tant que sujet
Fourier, Analyse de Voir les notices liées en tant que sujet
Algorithmes Voir les notices liées en tant que sujet
Mathématiques de l'ingénieur Voir les notices liées en tant que sujet
Approximation, Théorie de l' Voir les notices liées en tant que sujet