Optimal Control of Flow and Transport Equation Using Discontinuous Galerkin Methods
Master of Arts
This thesis analyzes the accuracy of discontinuous Galerkin methods for solving optimal control problems for flow and transport equations. I derive the optimality conditions for each optimal control problem and I derive error estimates for an optimal control problem constrained by a system of steady-state partial differential equations. Synthetic data is used to create numerical examples that verify the methods work. I then derive the optimality conditions for the optimal control of the miscible displacement equations, where the control is the flow rate of the injection fluid.
Miscible displacement; discontinuous Galerkin; optimal control