Computational Geosciences

, Volume 8, Issue 3, pp 255–299 | Cite as

A mixed finite element approach for viscoelastic wave propagation

  • Eliane Bécache
  • Abdelaâziz Ezziani
  • Patrick Joly
Article

Abstract

In this paper, we are interested in the modeling of wave propagation in viscoelastic media. We present a family of models which generalize the Zener’s model. We achieve its mathematical analysis: existence and uniqueness of solutions, energy decay and propagation with finite speed. For the numerical resolution, we extend a mixed finite element method proposed in [8]. This method combines mass lumping with a centered explicit scheme for time discretization. For the resulting scheme, we prove a discrete energy decay result and provide a sufficient stability condition. For the numerical simulation in open domains we adapt the perfectly matched layers techniques to viscoelastic waves [23]. Various numerical results are presented.

Keywords

energy dissipation finite velocity propagation mixed finite element stability analysis viscoelastic waves Zener’s model 

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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Eliane Bécache
    • 1
  • Abdelaâziz Ezziani
    • 1
  • Patrick Joly
    • 1
  1. 1.INRIA RocquencourtLe Chesnay CedexFrance

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