SUMMARYAn explicit predictor-corrector algorithm is derived from the implicit a-method. This explicit algorithm is shown to have better stability and accuracy properties than its Newmark-based predecessor. This algorithm is then combined with the implicit a-method, resulting in an implicit-explicit a-method which can be effectively utilized for linear and non-linear structural dynamics calculations.

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 Babugka-Brezzi theory and numerical results confirm these estimates as well as the good accuracy and stability of the method.

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