Consistent discontinuous finite elements in elastodynamics Original Research Article

Finite element discontinuities with respect to time have recently been extremely used in elastodynamic problems due to their natural utilization in combination with adaptive methods and their efficiency in discontinuity capturing techniques for non-smooth problems. In this work, we present some theoretical aspects and numerical results concerning the use of spatial discontinuities in a consistent finite element method for the same class of problems. We first review some formulations for the elastostatic problem and prove two Korn-like inequalities which are very useful for the derivation of convergence rates in Sobolev norms. Next, we present formulations for the dynamic case along with comments on their properties and estimates of convergence rates for smooth solutions, followed by numerical investigations of a typically non-smooth problem involving classical and emerging variational formulations. We also show some numerical experiments with finite element spaces enriched by discontinuous functions other than piecewise Lagrangian polynomials.