English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we discuss the numerical solution of elliptic distributedoptimal control problems with state or control constraints when the control isconsidered in the energy norm. As in the unconstrained case we can relate theregularization parameter and the finite element mesh size in order to ensure anoptimal order of convergence which only depends on the regularity of the giventarget, also including discontinuous target functions. While in most cases,state or control constraints are discussed for the more common $L^2$regularization, much less is known in the case of energy regularizations. Butin this case, and for both control and state constraints, we can formulatefirst kind variational inequalities to determine the unknown state, from wichwe can compute the control in a post processing step. Related variationalinequalities also appear in obstacle problems, and are well established bothfrom a mathematical and a numerical analysis point of view. Numerical resultsconfirm the applicability and accuracy of the proposed approach.

Regularization and finite element error estimates for elliptic  distributed optimal control problems with energy regularization and state or  control constraints