  We investigate the problem of guaranteed estimation of values of linear
continuous functionals defined on solutions to mixed variational equations
generated by linear elliptic problems from indirect noisy observations of these
solutions. We assume that right-hand sides of the equations, as well as the
second moments of noises in observations are not known; the only available
information is that they belong to given bounded sets in the appropriate
functional spaces. We look for linear with respect to observations optimal
estimates of solutions of aforementioned equations called minimax or guaranteed
estimates. We develop constructive methods for finding these estimates and
estimation errors which are expressed in terms of solutions to special mixed
variational equations and prove that Galerkin approximations of the obtained
variational equations converge to their exact solutions.
  We study also the problem of guaranteed estimation of right-hand sides of
mixed variational equations.
