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

種類:

電子ブック

責任表示:

by Aurora Marica, Enrique Zuazua

出版情報:

New York, NY : Springer New York : Imprint: Springer, 2014

著者名:

• Marica, Aurora
• Zuazua, Enrique
• SpringerLink (Online service)

シリーズ名:

SpringerBriefs in Mathematics ;

ISBN:

9781461458111 [1461458110]    

注記:

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 fi

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