A Weighted Least‐Squares Mixed Finite Element Formulation for Quasi‐Incompressible Elastodynamics

The purpose of this work is the application of the least‐squares finite element method to an elastodynamic, quasi‐incompressible problem under small strain assumptions. Therefore a mixed finite element based on a weighted least‐squares formulation is developed. The L 2 ‐norm minimization of the time‐discretized residuals of the given first‐order system of partial differential equations leads to a functional depending on displacements and stresses. In the numerical example the proposed mixed element is compared to an alternative approach, which is based on a least‐squares mixed finite element with improved momentum balance, see [1]. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)