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We investigate the problem of guaranteed estimation of values of linearcontinuous functionals defined on solutions to mixed variational equationsgenerated by linear elliptic problems from indirect noisy observations of thesesolutions. We assume that right-hand sides of the equations, as well as thesecond moments of noises in observations are not known; the only availableinformation is that they belong to given bounded sets in the appropriatefunctional spaces. We look for linear with respect to observations optimalestimates of solutions of aforementioned equations called minimax or guaranteedestimates. We develop constructive methods for finding these estimates andestimation errors which are expressed in terms of solutions to special mixedvariational equations and prove that Galerkin approximations of the obtainedvariational equations converge to their exact solutions.  We study also the problem of guaranteed estimation of right-hand sides ofmixed variational equations.

Mixed variational approach to finding guaranteed estimates from  solutions and right-hand sides of the second-order linear elliptic equations  under incomplete data