Error estimates of variational discretization and mixed finite element methods for semilinear parabolic optimal control problems

2011 ◽  
Author(s):  
Zuliang Lu ◽  
Xiao Huang
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
Finite Element Methods ◽  
Optimal Control Problems ◽  
Mixed Finite Element ◽  
Control Problems ◽  
Variational Discretization ◽  
Parabolic Optimal Control ◽  
Semilinear Parabolic

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 Error estimates of variational discretization for semilinear parabolic optimal control problems

2021 ◽  
Vol 6 (1) ◽  
pp. 772-793
Author(s):  
Chunjuan Hou ◽  
◽  
Zuliang Lu ◽  
Xuejiao Chen ◽  
Fei Huang ◽  
...  
Keyword(s):  
Optimal Control ◽  
Error Estimates ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Variational Discretization ◽  
Parabolic Optimal Control ◽  
Semilinear Parabolic
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