Discontinuous Galerkin approximations for an optimal control problem of three-dimensional Navier–Stokes–Voigt equations

Abstract

We analyze a fully discrete scheme based on the discontinuous (in time) Galerkin approach, which is combined with conforming finite element subspaces in space, for the distributed optimal control problem of the three-dimensional Navier–Stokes–Voigt equations with a quadratic objective functional and box control constraints. The space-time error estimates of order $$O(\sqrt{\tau }+h)$$ , where $$\tau $$ and h are respectively the time and space discretization parameters, are proved for the difference between the locally optimal controls and their discrete approximations.