A posteriori $$L^{\infty }(L^{\infty })$$-error estimates for finite-element approximations to parabolic optimal control problems

2021 ◽  
Vol 40 (8) ◽  
Author(s):  
Ram Manohar ◽  
Rajen Kumar Sinha
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
Optimal Control Problems ◽  
Control Problems ◽  
A Posteriori ◽  
Finite Element Approximations ◽  
Parabolic Optimal Control

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.

A Posteriori Error Estimates of Lowest Order Raviart-Thomas Mixed Finite Element Methods for Bilinear Optimal Control Problems

2012 ◽  
Vol 2 (2) ◽  
pp. 108-125 ◽  
Author(s):  
Zuliang Lu ◽  
Yanping Chen ◽  
Weishan Zheng
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
Optimal Control Problems ◽  
Mixed Finite Element ◽  
A Posteriori Error Estimates ◽  
Control Problems ◽  
Adaptive Finite Element ◽  
A Posteriori ◽  
Element Discretization

AbstractA Raviart-Thomas mixed finite element discretization for general bilinear optimal control problems is discussed. The state and co-state are approximated by lowest order Raviart-Thomas mixed finite element spaces, and the control is discretized by piecewise constant functions. A posteriori error estimates are derived for both the coupled state and the control solutions, and the error estimators can be used to construct more efficient adaptive finite element approximations for bilinear optimal control problems. An adaptive algorithm to guide the mesh refinement is also provided. Finally, we present a numerical example to demonstrate our theoretical results.

Sign in / Sign up

Export Citation Format

Share Document