A general setting is proposed for the mixed finite element approximations of
elliptic differential problems involving a unilateral boundary condition. The
treatment covers the Signorini problem as well as the unilateral contact
problem with or without friction. Existence, uniqueness for both the
continuous and the discrete problem as well as error estimates are established
in a general framework. As an application, the approximation of the Signorini
problem by the lowest order mixed finite element method of Raviart–Thomas is
proved to converge with a quasi-optimal error bound.
