Semi-Discrete and Fully Discrete Mixed Finite Element Methods for Maxwell Viscoelastic Model of Wave Propagation (Advances in Applied Mathematics and Mechanics, 2022)
Semi-discrete and fully discrete mixed finite element methods are considered for Maxwell-model-based problems of wave propagation in linear viscoelasticsolid. This mixed finite element framework allows the use of a large class of existing mixed conforming finite elements for elasticity in the spatial discretization. In thefully discrete scheme, a Crank-Nicolson scheme is adopted for the approximation ofthe temporal derivatives of stress and velocity variables. Error estimates of the semi-discrete and fully discrete schemes, as well as an unconditional stability result for thefully discrete scheme, are derived. Numerical experiments are provided to verify thetheoretical results.