  This paper considers semi-discrete and fully discrete mixed finite element
discretizations for Maxwell-model-based problems of wave propagation in
2-dimensional linear viscoelastic solid. A large class of existing mixed
conforming finite elements for elasticity are used in the spatial
discretization. In the fully discrete scheme, a Crank-Nicolson scheme is
adopted for the approximation of the temporal derivatives of displacement and
stress. Error estimates of the two schemes, as well as an unconditional
stability result for the fully discrete scheme, are derived. Numerical
experiments are provided which apply two low order rectangular elements in the
spatial discretization.
