The main aim of this paper is to consider the numerical approximation of mildly nonlinear elliptic problems by means of finite element methods of mixed type. The technique is based on an extended variational principle, in which the constraint of interelement continuity has been removed at the expense of introducing a Lagrange multiplier.

It is shown that the saddle point, which minimizes the energy functional over the product space, is characterized by the variational equations. The eauivalence is used in deriving the error estimates for the finite element approximations. We give an example of a mildly nonlinear elliptic problem and show how the error estimates can be obtained from the general results.