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

T. AKMAN1, B. KARASOZEN2, Z. KANAR-SEYMEN

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Abstract

The streamline upwind/Petrov Galerkin (SUPG) nite element method is studied for distributed optimal control problems governed by unsteady diusion-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 conrm the theoretically observed convergence rates.

Keywords

optimal control problems, unsteady diusion-convection-reaction equations, nite element elements, a priori error estimates.