Distributed optimal control of time-dependent diffusion–convection–reaction equations using space–time discretization

We apply two different strategies for solving unsteady distributed optimal control problems governed by diffusion–convection–reaction equations. In the first approach, the optimality system is transformed into a biharmonic equation in the space–time domain. The system is then discretized in space and time simultaneously and solved by an equation-based finite element package, i.e., COMSOL Multiphysics. The second approach is a classical gradient-based optimization method to solve the state and adjoint equations and the optimality condition iteratively. The convection-dominated state and adjoint equations are stabilized using the streamline upwind/Petrov–Galerkin (SUPG) method. Numerical results show favorable accuracy and efficiency of the two strategies for unstabilized and stabilized numerical solutions.