Filtering Mechanisms

  • Aurora Marica
  • Enrique Zuazua
Chapter
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

In this chapter, we design several filtering strategies for the discontinuous Galerkin approximations of the wave and Klein–Gordon equations based on the classical Fourier truncation method or on the bi-grid filtering algorithm. We rigorously prove their efficiency to recover the uniform observability estimates as the mesh size parameter goes to zero. In the last section of this chapter, we present several numerical simulations showing in particular how solutions corresponding to bi-grid projections of highly oscillatory Gaussian profiles split into several wave packets.

Keywords

Radon 

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Copyright information

© Aurora Marica, Enrique Zuazua 2014

Authors and Affiliations

  • Aurora Marica
    • 1
  • Enrique Zuazua
    • 2
  1. 1.Institute of Mathematics and Scientific ComputingUniversity of GrazGrazAustria
  2. 2.BCAM-Basque Center for Applied Mathematics IkerbasqueBilbaoSpain

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