scholarly journals Finite element methods for one dimensional elliptic distributed optimal control problems with pointwise constraints on the derivative of the state

2020 ◽  
Author(s):  
S. C. Brenner ◽  
L.-Y. Sung ◽  
W. Wollner
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Finite Element Methods ◽  
Optimal Control Problems ◽  
The State ◽  
Control Problems ◽  
Distributed Optimal Control ◽  
One Dimensional ◽  
Distributed Optimal Control Problems ◽  
Pointwise Constraints

A Posteriori Error Estimates of Semidiscrete Mixed Finite Element Methods for Parabolic Optimal Control Problems

2015 ◽  
Vol 5 (1) ◽  
pp. 85-108 ◽  
Author(s):  
Yanping Chen ◽  
Zhuoqing Lin
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
Finite Element Methods ◽  
Optimal Control Problems ◽  
Mixed Finite Element ◽  
Mixed Finite Element Methods ◽  
The State ◽  
Control Problems ◽  
A Posteriori

AbstractA posteriori error estimates of semidiscrete mixed finite element methods for quadratic optimal control problems involving linear parabolic equations are developed. The state and co-state are discretised by Raviart-Thomas mixed finite element spaces of order k, and the control is approximated by piecewise polynomials of order k (k ≥ 0). We derive our a posteriori error estimates for the state and the control approximations via a mixed elliptic reconstruction method. These estimates seem to be unavailable elsewhere in the literature, although they represent an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

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.

Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations

2016 ◽  
Vol 8 (6) ◽  
pp. 1050-1071 ◽  
Author(s):  
Tianliang Hou ◽  
Li Li
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
Elliptic Equations ◽  
Optimal Control Problems ◽  
Mixed Finite Element ◽  
Control Variable ◽  
The State ◽  
Control Problems ◽  
General Elliptic

AbstractIn this paper, we investigate the error estimates of mixed finite element methods for optimal control problems governed by general elliptic equations. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We derive L2 and H–1-error estimates both for the control variable and the state variables. Finally, a numerical example is given to demonstrate the theoretical results.

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