Stability analysis of linear multistep methods for classical elastodynamics Original Research Article

We propose an analysis of the stability of linear multistep methods when they are employed for the numerical integration in time of the equations resulting from the finite element spatial discretization of the problem of linear elastodynamics. First, the notion of stability is defined for the global equations of the space–time discrete problem. Second, a spectral analysis is employed to identify simpler modal criteria that are necessary and sufficient for stability. These new criteria are stronger than the classical spectral stability criterion which, furthermore, is shown not to be sufficient for global energy stability. The results of the analysis are applied to the study of several widely employed linear multistep integrators.