A new family of stable elements for nearly incompressible elasticity based on a mixed Petrov-Galerkin finite element formulation

Summary Adding to the classical Hellinger Reissner formulation another residual form of the equilibrium equation, a new Petrov-Galerkin finite element method is derived. It fits within the framework of a mixed finite element method and is proved to be stable for rather general combinations of stress and displacement interpolations, including equal-order discontinuous stress and continuous displacement interpolations which are unstable within the Galerkin approach. Error estimates are presented using the Babuka-Brezzi theory and numerical results confirm these estimates as well as the good accuracy and stability of the method.Dedicated to Professor Ivo Babuka on the occasion of his sixtieth birthdayPrepared for the conference on: The Impact of Mathematical Analysis on the Solution of Engineering Problems. University of Maryland, September 1986.