scholarly journals P 1 finite element methods for an elliptic optimal control problem with pointwise state constraints

2018 ◽  
Vol 40 (1) ◽  
pp. 1-28 ◽  
Author(s):  
Susanne C Brenner ◽  
Li-yeng Sung ◽  
Joscha Gedicke
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Finite Element Methods ◽  
State Constraints ◽  
Distributed Optimal Control ◽  
Pointwise State Constraints ◽  
Elliptic Optimal Control Problem ◽  
Elliptic Optimal Control

Abstract We present theoretical and numerical results for two $P_1$ finite element methods for an elliptic distributed optimal control problem on general polygonal/polyhedral domains with pointwise state constraints.

A 𝑃1 Finite Element Method for a Distributed Elliptic Optimal Control Problem with a General State Equation and Pointwise State Constraints

2021 ◽  
Vol 21 (4) ◽  
pp. 777-790
Author(s):  
Susanne C. Brenner ◽  
Sijing Liu ◽  
Li-Yeng Sung
Keyword(s):  
Finite Element Method ◽  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Control Problem ◽  
State Constraints ◽  
State Equation ◽  
Pointwise State Constraints ◽  
Primal Dual ◽  
Element Method

Abstract We investigate a P 1 P_{1} finite element method for an elliptic distributed optimal control problem with pointwise state constraints and a state equation that includes advective/convective and reactive terms. The convergence of this method can be established for general polygonal/polyhedral domains that are not necessarily convex. The discrete problem is a strictly convex quadratic program with box constraints that can be solved efficiently by a primal-dual active set algorithm.

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