Title: Optimal boundary control for time-dependent diffusion-convection-reaction equations

Authors: Zahire Seymen; Bülent Karasözen

Addresses: Department of Mathematics, Middle East Technical University, 06500, Ankara, Turkey ' Department of Mathematics, Middle East Technical University, 06500, Ankara, Turkey

Abstract: We study the boundary control problem governed by diffusion-convection-reaction equations with and without control constraints. The optimality system is transformed into a biharmonic equation in the space-time domain. The system is then discretised in space and time simultaneously and solved by an equation-based finite element package. The convection dominated state and adjoint equations are stabilised using the streamline upwind/Petrov Galerkin (SUPG) method. Numerical results for Robin type boundary conditions are presented with and without stabilisation.

Keywords: optimal boundary control; stabilised finite elements; convection dominated problems; control constraints; COMSOL multiphysics; time dependence; diffusion-convection-reaction equations; finite element method; FEM.

DOI: 10.1504/IJMMNO.2013.056543

International Journal of Mathematical Modelling and Numerical Optimisation, 2013 Vol.4 No.3, pp.282 - 300

Received: 25 Feb 2013
Accepted: 02 Jul 2013

Published online: 25 Sep 2013 *

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