Mixed stabilized finite element methods in linear elasticity for the velocity–stress equations in the time and the frequency domains

Abstract

In this work we present stabilized finite element methods for the mixed velocity–stress elasticity equations and for its irreducible velocity form. This is done both for the time and frequency domains, the latter being obtained by assuming a harmonic behavior in time. Stabilization methods that belong to the computational framework of the Variational Multi-Scale formulation are used. It is shown that the adequate selection of the algorithmic parameters on which the formulation depends allows one to switch from the primal to the dual functional framework. The performance of the method is tested through several numerical examples, one of which includes a convergence study.