A remark on second order methods in control of fluid flow

Abstract

AbstractWe present the functional analytic framework for a tracking‐type control problem of the instationary Navier‐Stokes equations. As solution methods for the control problem we comparatively discuss Newton's method as an example of the black box approach, and the SQP‐method as one of the all‐at‐once methods. It is argued that black box approaches in general outperform all‐at‐once methods since the numerical effort necessary to numerically solve linearizations of the instationary Navier‐Stokes equations compares to that of the nonlinear Navier‐Stokes system. We report a numerical comparison which illustrates our argumentation. For both approaches local convergence results are cited.