Robust Preconditioning: Optimal control of the convection-diffusion equation with limited observation
MSc Jarle SognOct. 6, 2020, 1:30 p.m. S2 054
We consider an optimization problem with a Convection-Diffusion-Reaction equation as constraint. A Schur complement preconditioner is proposed and we show that the problem is well-posed. The proposed preconditioner is robust with respect to all the problem parameters and the condition number of the preconditioned problem bounded by 4.05. We provide conditions for inf-sup stable discretizations and show one such discretization for box domains with constant convection. For this discretization, we derive error estimates. Finally, we provide numerical example highlighting the method.