A general setting is proposed for the mixed finite element approximations ofelliptic differential problems involving a unilateral boundary condition. Thetreatment covers the Signorini problem as well as the unilateral contactproblem with or without friction. Existence, uniqueness for both thecontinuous and the discrete problem as well as error estimates are establishedin a general framework. As an application, the approximation of the Signoriniproblem by the lowest order mixed finite element method of Raviart–Thomas isproved to converge with a quasi-optimal error bound.
