scholarly journals Crank–Nicolson finite element methods using symmetric stabilization with an application to optimal control problems subject to transient advection–diffusion equations

2011 ◽  
Vol 9 (1) ◽  
pp. 319-329 ◽  
Author(s):  
Erik Burman
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Finite Element Methods ◽  
Optimal Control Problems ◽  
Diffusion Equations ◽  
Control Problems ◽  
Advection Diffusion ◽  
Crank Nicolson

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.

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