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Summary. We consider a class of equilibrium finite element methods for elasticity problems. The approximate stresses satisfy the equilibrium equations but the symmetry of the stress tensor is relaxed. Optimal error bounds for the stresses and numerical examples are given.

The paper is devoted to the construction of finite element methods for 2nd order elliptic equations based on a primal hybrid variational principle. Optimal error bounds are proved. As a corollary, we obtain a general analysis of nonconforming finite element methods.