A mixed finite element approach for a factional viscoelastic wave propagation in-time-domain

M. Ait Ichou () and A. Ezziani
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M. Ait Ichou: ENS, Hassan II University of
A. Ezziani: FSJES AebaHassan II University

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 1, 79-98

Abstract: Abstract In this paper, we present a numerical approximation of fractional order viscoelastic wave equation in the 2D case. These viscoelastic models are shown to be effective in modeling wave attenuation, in particular the Q-factor approximation, when previously shown in our work [1]. The novelty of this study is the numerical simulation of the propagation of viscoelastic waves with the fractional Zener model in the space-time domain, moreover, we use real data. For the numerical resolution, we used a mixed finite element method. This method combines the mass lumping with centered explicit scheme for time discretization. For the resulting scheme, we prove a discrete energy decay result and provide a sufficient stability condition. Various numerical results are presented for the model.

Keywords: Fractional derivative; Mixed finite element; Energy dissipation; Stability analysis; Viscoelastic wave propagation; Zener’s model (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-023-00461-8

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