Mixed Finite Element Methods for Elastodynamics Problems in the Symmetric Formulation (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, we analyze semi-discrete and fully discrete mixed finite elementmethods for linear elastodynamics problems in the symmetric formulation. Fora large class of conforming mixed finite element methods, the error estimates for eachscheme are derived, including the energy norm and $L^2$ norm for stress, and the $L^2$ norm for velocity. All the error estimates are robust for the nearly incompressible materials,in the sense that the constant bound and convergence order are independentof Lamé constant λ. The stress approximation in both norms, as well as the velocityapproximation in $L^2$ norm, are with optimal convergence order. Finally numericalexperiments are provided to confirm the theoretical analysis.