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

• Autores: Tugba Akman, Bülent Karasözen
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 272, Nº 1, 2014, págs. 41-56
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.05.002
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• Resumen

  • 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-thendiscretize 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.