Estimates of deviations from exact solution of the generalized Oseen problem

The paper is concerned with a generalized version of the stationary Oseen problem, which often arises in semidiscrete approximation methods used for quantitative analysis of Navier–Stokes equations. We derive a fully computable functional defined for admissible velocity, stress, and pressure fields and prove that this functional generates upper and lower bounds of the total error evaluated in the corresponding combined norm. Moreover, this functional vanishes if and only if its arguments coincide with the exact velocity, stress, and pressure. Therefore, minimization of it is equivalent to solving the Oseen problem.