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A mixed finite element approach for viscoelastic wave propagation

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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.

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  1. INRIA Rocquencourt, B.P. 105, 78153, Le Chesnay Cedex, France

    Eliane Bécache, Abdelaâziz Ezziani & Patrick Joly

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  1. Eliane Bécache
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  2. Abdelaâziz Ezziani
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  3. Patrick Joly
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Bécache, E., Ezziani, A. & Joly, P. A mixed finite element approach for viscoelastic wave propagation. Comput Geosci 8, 255–299 (2005). https://doi.org/10.1007/s10596-005-3772-8

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