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In this paper we show how to find the exact error (not just an estimate ofthe error) of a conforming mixed approximation by using the functional type aposteriori error estimates in the spirit of Repin. The error is measured in amixed norm which takes into account both the primal and dual variables. Wederive this result for elliptic partial differential equations of a certainclass. We first derive a special version of our main result by using asimplified reaction-diffusion problem to demonstrate the strong connection tothe classical functional a posteriori error estimates of Repin. After this wederive the main result in an abstract setting. Our main result states that inorder to obtain the exact global error value of a conforming mixedapproximation one only needs the problem data and the mixed approximation ofthe exact solution. There is no need for calculating any auxiliary data. Thecalculation of the exact error consists of simply calculating two (usuallyintegral) quantities where all the quantities are known after the approximatesolution has been obtained by any conforming method. We also show somenumerical computations to confirm the results.

Functional A Posteriori Error Equalities for Conforming Mixed Approximations of Elliptic Problems