A stabilized mixed finite element method for finite elasticity.: Formulation for linear displacement and pressure interpolation Original Research Article

A stabilized mixed finite element method for finite elasticity is presented. The method circumvents the fulfillment of the Ladyzenskaya–Babuska–Brezzi condition by adding mesh-dependent terms, which are functions of the residuals of the Euler–Lagrange equations, to the usual Galerkin method. The weak form and the linearized weak form are presented in terms of the reference and current configuration. Numerical experiments using a tetrahedral element with linear shape functions for the displacements and for the pressure show that the method successfully yields a stabilized element.