Error estimates for an unregularized optimal control problem for the stationary Navier-Stokes equations
Numerical Analysis
2026-05-26 v2 Numerical Analysis
Optimization and Control
Abstract
We consider an unregularized optimal control problem subject to the steady-state Navier-Stokes equations. We derive the existence of optimal solutions and prove first- and second-order optimality conditions. To approximate solutions to the optimal control problem, we consider the variational discretization scheme. We analyze convergence properties of the discretization and prove a priori error estimates for locally optimal controls that are nonsingular and which satisfy a growth condition which implies a bang-bang structure. We also propose a residual-type a posteriori error estimator that accounts for the discretization of the state and adjoint equations, and prove suitable reliability properties for such an error estimator.
Cite
@article{arxiv.2605.01633,
title = {Error estimates for an unregularized optimal control problem for the stationary Navier-Stokes equations},
author = {Francisco Fuica and Nicolai Jork},
journal= {arXiv preprint arXiv:2605.01633},
year = {2026}
}