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Semi-discrete and fully discrete mixed finite element methods are consideredfor Maxwell-model-based problems of wave propagation in linear viscoelasticsolid. This mixed finite element framework allows the use of a large class ofexisting mixed conforming finite elements for elasticity in the spatialdiscretization. In the fully discrete scheme, a Crank-Nicolson scheme isadopted for the approximation of the temporal derivatives of stress andvelocity variables. Error estimates of the semi-discrete and fully discreteschemes, as well as an unconditional stability result for the fully discretescheme, are derived. Numerical experiments are provided to verify thetheoretical results.

Semi-discrete and fully discrete mixed finite element methods for Maxwell viscoelastic model of wave propagation