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

Akman T., KARASÖZEN B., Kanar-Seymen Z.

TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, vol.7, no.2, pp.221-235, 2017 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 2
  • Publication Date: 2017
  • Journal Name: TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
  • Page Numbers: pp.221-235
  • Middle East Technical University Affiliated: Yes

Abstract

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.