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We analyze the application to elastodynamic problems of mixed finite element methods for elasticity with weakly imposed symmetry of stress. Our approach leads to a semidiscrete method which consists of a system of ordinary differential equations without algebraic constraints. Our error analysis, which is based on a new elliptic projection operator, applies to several mixed finite element spaces developed for elastostatics. The error estimates we obtain are robust for nearly incompressible materials. [ABSTRACT FROM AUTHOR]

A large variety of discretizations have been proposed in the literature for the numerical solution of the dynamic Signorini problem. We classify the different discretizations into four groups. The first three groups correspond to different ways of enforcing the contact condition: exact enforcement, enforcement with penalty, and enforcement with contact condition in velocity. The fourth approach is based on a modification of the mass matrix. Numerical simulations on two one-dimensional benchmark problems with analytical solutions illustrate the properties of representative methods within each class, focusing first on spurious oscillations triggered by contact and then on energy behavior after multiple impacts. Selected schemes are also tested on a two-dimensional benchmark. [ABSTRACT FROM AUTHOR]

We study a finite element-based space-time discretization of the elastodynamics equation uϵtt - div σ(∇uϵ) - eΔ?uϵt = 0 for ϵ ≥ 0, where σ = Dφ and φ is a nonconvex function. The convergence for regularization parameters ϵ > 0 of iterates to weak solutions and for the limiting problem e = 0 of iterates towards generalized solutions is shown in a general setting of data. Computational experiments are included to motivate formation and propagation of two-dimensional microstructures for decreasing values of the regularization parameter. [ABSTRACT FROM AUTHOR]