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

The streamline upwind/Petrov Galerkin (SUPG) finite element method is studied for distributed optimal control problems governed by unsteady diffusion-convection-reaction equations with control constraints. We derive stability and convergence estimates for fully-discrete state, adjoint and control an...

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Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 7; no. 2; p. 221
Main Authors Akman, T, Karasozen, B, Kanar-Seymen, Z
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.12.2017
Elman Hasanoglu
Subjects
Control stability
Control theory
Convection
Convergence
Convergence (Mathematics)
Economic models
Equations (Mathematics)
Finite element method
Galerkin method
Industrial equipment
Mathematical research
Optimal control
Pollution control
Steel
Time dependence
Water pollution
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Summary:The streamline upwind/Petrov Galerkin (SUPG) finite element method is studied for distributed optimal control problems governed by unsteady diffusion-convection-reaction 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 confirm the theoretically observed convergence rates.Keywords: optimal control problems, unsteady diffusion-convection-reaction equations, finite element elements, a priori error estimates.AMS Subject Classification: 49N10,49K20, 65M60,65M15.
ISSN:2146-1147
2146-1147