Control Strategies for Fluid Flows - Optimal Versus Suboptimal Control

In our talk optimal and suboptimal distributed and boundary control strategies for uid ows governed by the Navier-Stokes equation (NSE) together with some aspects of the numerical and practical implementation of the underlying algorithms will be addressed. The objective of our numerical investigations is to compare optimal and suboptimal control strategies with regard to cost reduction and numerical expense for backward facing step ows. To describe the approach let IR 2 (IR 3) denote the ow region with boundary ? = ?c ? obs ? d , where in the case of boundary control ?c denotes the part of the boundary where control is applied, ? obs is the observation boundary and ? d is the remaining part of the boundary part where xed Dirichlet data are prescribed. For the case of boundary control and boundary observations the control problem is given by (P)