Parameter-Robust Preconditioning for Oseen Iteration Applied to Stationary and Instationary Navier--Stokes Control

Optimal and instantaneous control of the instationary Navier-Stokes equations

Contents Danksagung 1 Chapter 1. Introduction 5 1. Aims and scope of flow control 5 2. A brief review in active flow control 8 Chapter 2. Notation and preliminary results 15 1. Quasi-Stokes problems 15 2. Instationary Navier-Stokes equations in 2d 16 3. Navier-Stokes numerics 19 Chapter 3. Optimal control of the instationary Navier-Stokes equations 23 1. The optimal control problem 23 2. Deriva...

A SQP-Semismooth Newton-type Algorithm applied to Control of the instationary Navier--Stokes System Subject to Control Constraints

Sequential quadratic programming (SQP) methods for the optimal control of the instationary Navier-Stokes equations with pointwise constraints on the control are considered. Due to the presence of the constraints the quadratic subproblems (QP) of SQP require a more sophisticated solver compared to the unconstrained case. In this paper, a semismooth Newton method is proposed for efficiently solvi...

Robust Preconditioning for XFEM Applied to Time-Dependent Stokes Problems

We consider a quasi-stationary Stokes interface problem with a reaction term proportional to τ = 1/∆t ≥ 0 as obtained by a time discretization of a time-dependent Stokes problem. The mesh used for space discretization is not aligned with the interface. We use the P1 extended finite element space for the pressure approximation and the standard conforming P2 finite element space for the velocity ...

Optimal control of Navier-Stokes equations by Oseen approximation

A non-standard sequential-quadratic-programming-type iterational process based on Oseen’s approximation is proposed and analyzed to solve an optimal control problem for the steady-state Navier-Stokes equations. Further numerical approximation by a finite-element method and sample computational experiments are presented, too.

The SQP-method for tracking type control of the instationary Navier-Stokes equations