Keywords: flow control, analytic solution
Global classification: linear-quadratic, convex
Functional: convex quadratic
Geometry: easy, fixed
Design: coupled via volume data
- linear elliptic operator of order 2.
- Defined on a 3-dim domain in 3-dim space
- No time dependence.
Submitted on 2013-01-04 by Arnd Rösch.
Published on 2013-01-04
We have a distributed optimal control problem for the Stokes equations with component-wise
box constraints for the distributed control. A diﬃculty in the construction of test examples as
the present one is the satisfaction of the divergence-free condition. Moreover, the example is
This problem and the analytical solution were published in Rösch and Vexler .
Variables & Notation
The following system for the state (velocity and pressure)
, the control
and the adjoint
state , given in
strong form, characterizes the unique minimizer. The projection is a component-wise projection onto
The optimal state, adjoint state and control are known analytically:
A. Rösch and B. Vexler. Optimal control of the Stokes equations: A priori error
analysis for ﬁnite element discretization with postprocessing. SIAM Journal on
Numerical Analysis, 44(5):1903–1920, 2006. doi: 10.1137/050637364.