Error estimates of triangular mixed finite element methods for quasilinear optimal control problems

2012 ◽  
Vol 7 (3) ◽  
pp. 397-413 ◽  
Author(s):  
Yanping Chen ◽  
Zuliang Lu ◽  
Ruyi Guo
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
Finite Element Methods ◽  
Optimal Control Problems ◽  
Mixed Finite Element ◽  
Mixed Finite Element Methods ◽  
Control Problems

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.

Error Estimates and Superconvergence of Mixed Finite Element Methods for Optimal Control Problems with Low Regularity

2012 ◽  
Vol 4 (06) ◽  
pp. 751-768 ◽  
Author(s):  
Yanping Chen ◽  
Tianliang Hou ◽  
Weishan Zheng
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
Finite Element Methods ◽  
Optimal Control Problems ◽  
Mixed Finite Element ◽  
Control Variable ◽  
Mixed Finite Element Methods ◽  
Control Problems ◽  
Elliptic Optimal Control

AbstractIn this paper, we investigate the error estimates and superconvergence property of mixed finite element methods for elliptic optimal control problems. 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 deriveL2andL∞-error estimates for the control variable. Moreover, using a recovery operator, we also derive some superconvergence results for the control variable. Finally, a numerical example is given to demonstrate the theoretical results.

scholarly journals A Priori Error Estimates of Mixed Finite Element Methods for General Linear Hyperbolic Convex Optimal Control Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Zuliang Lu ◽  
Xiao Huang
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
Finite Element Methods ◽  
Optimal Control Problems ◽  
Mixed Finite Element ◽  
A Priori ◽  
Mixed Finite Element Methods ◽  
Control Problems ◽  
Priori Error Estimates

The aim of this work is to investigate the discretization of general linear hyperbolic convex optimal control problems by using the mixed finite element methods. The state and costate are approximated by thekorder (k≥0) Raviart-Thomas mixed finite elements and the control is approximated by piecewise polynomials of orderk. By applying the elliptic projection operators and Gronwall’s lemma, we derive a priori error estimates of optimal order for both the coupled state and the control approximation.

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