Abstract

This article deals with an expanded mixed finite element formulation, based on the Hu-Washizu principle, for a nonlinear incompressible material in the plane. We follow our related previous works and introduce both the stress and the strain tensors as further unknowns, which yields a two-fold saddle point operator equation as the corresponding variational formulation. A slight generalization of the classical Babuška-Brezzi's theory is applied to prove unique solvability of the continuous and discrete formulations, and to derive the corresponding a priori error analysis. An extension of the well-known PEERS space is used to define an stable associated Galerkin scheme. Finally, we provide an a posteriori error analysis based on the classical Bank-Weiser approach. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 105-128, 2002.