Discontinuous Galerkin methods for time-dependent convection dominated optimal control problems


Thesis Type: Postgraduate

Institution Of The Thesis: Orta Doğu Teknik Üniversitesi, Institute of Applied Mathematics, Turkey

Approval Date: 2011

Student: TUĞBA AKMAN

Supervisor: BÜLENT KARASÖZEN

Abstract:

Distributed optimal control problems with transient convection dominated diffusion convection reaction equations are considered. The problem is discretized in space by using three types of discontinuous Galerkin (DG) method: symmetric interior penalty Galerkin (SIPG), nonsymmetric interior penalty Galerkin (NIPG), incomplete interior penalty Galerkin (IIPG). For time discretization, Crank-Nicolson and backward Euler methods are used. The discretize-then-optimize approach is used to obtain the finite dimensional problem. For one-dimensional unconstrained problem, Newton-Conjugate Gradient method with Armijo line-search. For two-dimensional control constrained problem, active-set method is applied. A priori error estimates are derived for full discretized optimal control problem. Numerical results for one and two-dimensional distributed optimal control problems for diffusion convection equations with boundary layers confirm the predicted orders derived by a priori error estimates.