Variational time discretization methods for optimal control problems governed by diffusion-convection-reaction equations. (English) Zbl 1293.49065
Summary: In this paper, a distributed optimal control problem governed by an unsteady diffusion-convection-reaction equation without control constraints is studied. Time discretization is performed by variational discretization using continuous and discontinuous Galerkin methods, while a symmetric interior penalty Galerkin method 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. Numerical results given for convection dominated problems via the optimize-then-discretize approach confirm the theoretically observed convergence rates.
MSC:
| 49M25 | Discrete approximations in optimal control |
| 49K20 | Optimality conditions for problems involving partial differential equations |
| 49N10 | Linear-quadratic optimal control problems |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
Keywords:
optimal control problems; unsteady diffusion-convection-reaction equation; variational time discretization; a priori error estimatesReferences:
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