Optimal control and inverse problems

Clason, Christian; Kaltenbacher, Barbara

doi:10.1088/1361-6420/ab8485

Cited by 3 publications

(1 citation statement)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Optimal control [2,10,17,22] and inverse problems [8,12,20] subject to partial differential equations often involve some parameter-dependent cost or regularization terms, see also the recent special issue [7] on optimal control and inverse problems. While in optimal control problems the regularization parameter is often considered as a given constant, in inverse problems, the parameter-dependent convergence as → 0 is well studied, see, e.g., [1].…”

Section: Introductionmentioning

confidence: 99%

An adaptive finite element method for distributed elliptic optimal control problems with variable energy regularization

Langer¹,

Löscher²,

Steinbach³

et al. 2022

Preprint

View full text Add to dashboard Cite

We analyze the finite element discretization of distributed elliptic optimal control problems with variable energy regularization, where the usual L 2 (Ω) norm regularization term with a constant regularization parameter is replaced by a suitable representation of the energy norm in H −1 (Ω) involving a variable, mesh-dependent regularization parameter (x). It turns out that the error between the computed finite element state u h and the desired state u (target) is optimal in the L 2 (Ω) norm provided that (x) behaves like the local mesh size squared. This is especially important when adaptive meshes are used in order to approximate discontinuous target functions. The adaptive scheme can be driven by the computable and localizable error norm u h − u L 2 (Ω) between the finite element state u h and the target u. The numerical results not only illustrate our theoretical findings, but also show that the iterative solvers for the discretized reduced optimality system are very efficient and robust.

show abstract