Mixed Finite Element Discretization for Maxwell Viscoelastic Model of Wave Propagation

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.