Mesh Adaptation for Stationary Flow Control

We consider local mesh adaptation for stationary flow control problems. The state equation is given by the incompressible Navier-Stokes equations with Neumann boundary control. As an example, the functional to be minimized is the drag coefficient of an immersed body. We use finite elements on locally refined meshes to discretize the first order necessary conditions based on the Lagrangian. An a posteriori error estimate is derived which is directly related to the control problem. It is used to successively enrich the finite element space until the computed solution satisfies prescribed accuracy requirements.