Streamline upwind/Petrov Galerkin solution of optimal control problems governed by time dependent diffusion-convection-reaction equations

The streamline upwind/Petrov Galerkin (SUPG) finite element method is studied for distributed optimal control problems governed by unsteady diffusion-convectionreaction equations with control constraints. We derive stability and convergence estimates for fully-discrete state, adjoint and control and discuss the choice of the stabilization parameter by applying backward Euler method in time. We show that by balancing the error terms in the convection dominated regime, optimal convergence rates can be obtained. The numerical results confirm the theoretically observed convergence rates.Publisher's Versio

Variational time discretization methods for optimal control problems governed by diffusion-convection-reaction equations

In this paper, the distributed optimal control problem governed by unsteady diffusion-convection-reaction equation without control constraints is studied. Time discretization is performed by variational discretization using continuous and discontinuous Galerkin methods, while symmetric interior penalty Galerkin with upwinding is used for space discretization. We investigate the commutativity properties of the optimize-then-discretize and discretize-then-optimize approaches for the continuous and discontinuous Galerkin time discretization. A priori error estimates are derived for fully-discrete state, adjoint and control. The numerical results given for convection dominated problems via optimize-then-discretize approach confirm the theoretically observed convergence rates