A Finite Element Method For The Approximation Of Waves In Fluid Saturated Poroviscoelastic Media.

Abstract

This work presents and analyzes a _nite element procedure for the simulation of
wave propagation in a porous solid saturated by a single-phase _uid. The equations of motion,
formulated in the space-frequency domain, include dissipation due to viscous interaction
between the _uid and solid phases and intrinsic anelasticity of the solid modeled using linear
viscoelasticity. This formulation leads to the solution of a Helmholtz-type boundary value
problem for each temporal frequency. For the spatial discretization, nonconforming _nite element
spaces are employed for the solid phase, while for the _uid phase the vector part of the
Raviart-Thomas-Nedelec mixed _nite element space is used. Optimal a priori error estimates
for a standard Galerkin _nite element procedure are derived.