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

This article is concerned with the nonconforming finite element method fordistributed elliptic optimal control problems with pointwise constraints on thecontrol and gradient of the state variable. We reduce the minimization probleminto a pure state constraint minimization problem. In this case, the solutionof the minimization problem can be characterized as fourth-order ellipticvariational inequalities of the first kind. To discretize the control problemwe have used the bubble enriched Morley finite element method. To ensure theexistence of the solution to discrete problems three bubble functionscorresponding to the mean of the edge are added to the discrete space. Wederive the error in the state variable in $H^2$-type energy norm. Numericalresults are presented to illustrate our analytical findings.

A nonconforming finite element method for an elliptic optimal control problem with constraint on the gradient