Optimal Control Problems for the Two Dimensional Rayleigh--Bénard Type Convection by a Gradient Method

Abstract

In this aricle, the author considers mathematical formulation and numerical solutions of distributed and Neumann boundary optimal control problems associated with the stationary Bénard problem. The solution of the optimal control problem is obtained by controlling of the source term of the equations and/or Neumann boundary conditions. Then the author considers the approximation, by finite element methods, of the optimality system and derive optimal error estimates. The convergence of a simple gradient method is proved and some numerical results are given.