Analysis of some low-order nonconforming mixed finite elements for linear elasticity problem

In this article we present and analyze some low-order nonconforming mixed finite elements for linear elasticity problem based on the PEERS formulation of Arnold et al. [I]. Optimal error estimates are established for the stress, the displacement and the rotation which are valid uniformly with respect to the Poisson ratio. We also apply the postprocessing technique of Arnold and Brezzi [9] to our nonconforming mixed finite elements, and show that after algebraic condensation, they are equivalent to some modified conforming and nonconforming finite element methods for the displacement formulation. (C) 2005 Wiley Periodicals, Inc.