On the stability and convergence of fully discrete solutions in linear elastodynamics Original Research Article

In this paper we analyze the numerical solution of problems in linear elastodynamics which combine finite elements in space and finite differences in time. After describing the continuum framework, we discuss the space-time discretization and we propose a convergence proof in the energy norm for the whole approximation. The modal analysis is used to provide a more convenient way to check for stability and consistency. The results of this analysis question the validity of the classical spectral criterion for the determination of the stability of space-time discretizations. Stronger conditions that guarantee energy stability for arbitrary initial conditions are proposed. Numerical simulations verifying these results are presented.