Finite Element Methods for Elliptic Distributed Optimal Control Problems with Pointwise State Constraints (Survey)

2020 ◽  
pp. 3-16
Author(s):  
Susanne C. Brenner
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Finite Element Methods ◽  
State Constraints ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Distributed Optimal Control ◽  
Pointwise State Constraints ◽  
Distributed Optimal Control Problems

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.

scholarly journals A Nitsche-eXtended Finite Element Method for Distributed Optimal Control Problems of Elliptic Interface Equations

2020 ◽  
Vol 20 (2) ◽  
pp. 379-393 ◽  
Author(s):  
Tao Wang ◽  
Chaochao Yang ◽  
Xiaoping Xie
Keyword(s):  
Finite Element Method ◽  
Optimal Control ◽  
Finite Element ◽  
Extended Finite Element Method ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Extended Finite Element ◽  
Distributed Optimal Control ◽  
Distributed Optimal Control Problems ◽  
Interface Equations

AbstractThis paper analyzes an interface-unfitted numerical method for distributed optimal control problems governed by elliptic interface equations. We follow the variational discretization concept to discretize the optimal control problems and apply a Nitsche-eXtended finite element method to discretize the corresponding state and adjoint equations, where piecewise cut basis functions around the interface are enriched into the standard linear element space. Optimal error estimates of the state, co-state and control in a mesh-dependent norm and the {L^{2}} norm are derived. Numerical results are provided to verify the theoretical results.

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