Numerical approximation of optimal control of fluid equations with buoyancy

摘要

The numerical approximation of an optimal control problem involving the Burgers' equation coupled with a heat equation is considered. The numerical scheme couples the finite element method with an iterative scheme based on a fixed point theorem to solve the partial differential equations. Introducing finite dimensional admissible control sets, we are able to solve numerically the optimal control problem. Convergence is proved utilizing the regularity result of the optimal controls established in [1].