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A mixed finite element approach for viscoelastic wave propagation.

Eliane Bécache 1 Abdelaâziz Ezziani 1 Patrick Joly 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
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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Submitted on : Friday, April 25, 2014 - 3:02:25 PM
Last modification on : Thursday, January 14, 2021 - 11:56:04 AM

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Eliane Bécache, Abdelaâziz Ezziani, Patrick Joly. A mixed finite element approach for viscoelastic wave propagation.. Computational Geosciences, Springer Verlag, 2004, 8 (3), pp.255-299. ⟨10.1007/s10596-005-3772-8⟩. ⟨hal-00983573⟩



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