STREAMLINE UPWIND/PETROV GALERKIN SOLUTION OF OPTIMAL CONTROL PROBLEMS GOVERNED BY TIME DEPENDENT DIFFUSION-CONVECTION-REACTION EQUATIONS

Abstract

The streamline upwind/Petrov Galerkin (SUPG) finite element method isstudied 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 balancingthe error terms in the convection dominated regime, optimal convergence rates can beobtained. The numerical results confirm the theoretically observed convergence rates