scholarly journals A posteriori error estimates for mixed finite element solutions of convex optimal control problems

2008 ◽  
Vol 211 (1) ◽  
pp. 76-89 ◽  
Author(s):  
Yanping Chen ◽  
Wenbin Liu
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
Optimal Control Problems ◽  
Mixed Finite Element ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Control Problems ◽  
A Posteriori ◽  
A Posteriori Error

scholarly journals Adaptive Mixed Finite Element Methods for Parabolic Optimal Control Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Zuliang Lu
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problems ◽  
Mixed Finite Element ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Control Problems ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Parabolic Optimal Control

We will investigate the adaptive mixed finite element methods for parabolic optimal control problems. The state and the costate are approximated by the lowest-order Raviart-Thomas mixed finite element spaces, and the control is approximated by piecewise constant elements. We derive a posteriori error estimates of the mixed finite element solutions for optimal control problems. Such a posteriori error estimates can be used to construct more efficient and reliable adaptive mixed finite element method for the optimal control problems. Next we introduce an adaptive algorithm to guide the mesh refinement. A numerical example is given to demonstrate our theoretical results.

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