scholarly journals A GLOBAL SUPERCONVERGENT L∞-ERROR ESTIMATE OF MIXED FINITE ELEMENT METHODS FOR SEMILINEAR ELLIPTIC OPTIMAL CONTROL PROBLEMS

2015 ◽  
Vol 5 (3) ◽  
pp. 313-328
Author(s):  
Li Li ◽  
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimate ◽  
Finite Element Methods ◽  
Optimal Control Problems ◽  
Mixed Finite Element ◽  
Control Problems ◽  
Semilinear Elliptic ◽  
Elliptic Optimal Control Problems ◽  
Elliptic Optimal Control

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.

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