Abstract
We consider standard tracking-type, distributed elliptic optimal control problems with L 2 L{2} regularization, and their finite element discretization. We are investigating the L2 L{2} error between the finite element approximation uh u_{\varrho h} of the state u q u_{\varrho} and the desired state (target) u\overline{u} in terms of the regularization parameter q and the mesh size h that leads to the optimal choice q = h 4 \varrho=h{4}. It turns out that, for this choice of the regularization parameter, we can devise simple Jacobi-like preconditioned MINRES or Bramble-Pasciak CG methods that allow us to solve the reduced discrete optimality system in asymptotically optimal complexity with respect to the arithmetical operations and memory demand. The theoretical results are confirmed by several benchmark problems with targets of various regularities including discontinuous targets.
Original language | English |
---|---|
Pages (from-to) | 989-1005 |
Number of pages | 17 |
Journal | Computational Methods in Applied Mathematics |
Volume | 23 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1 Oct 2023 |
Keywords
- Elliptic Optimal Control Problems
ASJC Scopus subject areas
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics