Finite element methods for the simulation of waves in composite saturated poroviscoelastic media

This work presents and analyzes a collection of finite element procedures for the simulation of wave propagation in a porous medium composed of two weakly coupled solids saturated by a single-phase fluid. The equations of motion, formulated in the space-frequency domain, include dissipation due to viscous interaction between the fluid and solid phases with a correction factor in the high-frequency range and intrinsic anelasticity of the solids 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 finite element spaces are employed for the solid phases, while for the fluid phase the vector part of the Raviart-Thomas-Nedelec mixed finite element space is used. Optimal a priori error estimates for global standard and hybridized Galerkin finite element procedures are derived. An iterative nonoverlapping domain decomposition procedure is also presented and convergence results are derived. Numerical experiments showing the application of the numerical procedures to simulate wave propagation in partially frozen porous media are presented.