Solving Distributed Optimal Control Problems for the Unsteady Burgers Equation in COMSOL Multiphysics®

F. Yilmaz[1] and B. Karasözen[2]

[1]Department of Mathematics, Gazi University, Ankara, Turkey
[2]Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey

We use COMSOL Multiphysics® for solving distributed optimal control of un- steady Burgers equation without constraints and with pointwise control constraints. Using the first order optimality conditions, we apply projection and semi-smooth Newton methods for solving the optimality system. We have applied the standard approach by integrating the state equation forward in time and the ad- joint equation backward in time using gradient method. We also consider the optimality system in the space-time cylinder as an elliptic equation and solve it adaptively. Numerical results computed by the gradient method, adaptive and non-adaptive elliptic solvers of COMSOL Multiphysics® are presented for both the unconstrained and the control constrained cases.