A stress-velocity least-squares mixed finite element formulation for incompressible elastodynamics

In the framework of solving elastodynamic problems using a least-squares mixed finite element method (LSFEM) the implementation of a stress-velocity formulation for small strains is introduced and discussed in the present contribution. The element formulation is based on a first-order div – grad system, with the balance equation of momentum and the constitutive law as the governing equations. Application of the L₂-norm to the two residuals leads to a functional depending on stresses and velocities. Different time discretization schemes are considered, a scalar weighting is introduced and chosen in dependency of the different time discretization methods. In a numerical example the influence of the time integration method, the chosen time step width and the related weighing factor are investigated for a two-dimensional problem. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)