  We consider a model problem of the scattering of linear acoustic waves in
free homogeneous space by an elastic solid. The stress tensor in the solid
combines the effect of a linear dependence of strains with the influence of an
existing electric field. The system is closed using Gauss's law for the
associated electric displacement. Well-posedness of the system is studied by
its reformulation as a first order in space and time differential system with
help of an elliptic lifting operator. We then proceed to studying a
semidiscrete formulation, corresponding to an abstract Finite Element
discretization in the electric and elastic fields, combined with an abstract
Boundary Element approximation of a retarded potential representation of the
acoustic field. The results obtained with this approach improve estimates
obtained with Laplace domain techniques. While numerical experiments
illustrating convergence of a fully discrete version of this problem had
already been published, we demonstrate some properties of the full model with
some simulations for the two dimensional case.
