scholarly journals ERROR ESTIMATES OF MIXED FINITE ELEMENT APPROXIMATIONS FOR A CLASS OF FOURTH ORDER ELLIPTIC CONTROL PROBLEMS

2013 ◽  
Vol 50 (4) ◽  
pp. 1127-1144 ◽  
Author(s):  
Tianliang Hou
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
Fourth Order ◽  
Mixed Finite Element ◽  
Control Problems ◽  
Finite Element Approximations ◽  
Elliptic Control Problems

Mixed Finite Element Methods for Fourth Order Elliptic Optimal Control Problems

2016 ◽  
Vol 9 (4) ◽  
pp. 528-548
Author(s):  
K. Manickam ◽  
P. Prakash
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
Fourth Order ◽  
Optimal Control Problems ◽  
Mixed Finite Element ◽  
Control Variable ◽  
The State ◽  
Control Problems ◽  
Element Discretization

AbstractIn this paper, a priori error estimates are derived for the mixed finite element discretization of optimal control problems governed by fourth order elliptic partial differential equations. The state and co-state are discretized by Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. The error estimates derived for the state variable as well as those for the control variable seem to be new. We illustrate with a numerical example to confirm our theoretical results.

Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations

2016 ◽  
Vol 8 (6) ◽  
pp. 1050-1071 ◽  
Author(s):  
Tianliang Hou ◽  
Li Li
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
Elliptic Equations ◽  
Optimal Control Problems ◽  
Mixed Finite Element ◽  
Control Variable ◽  
The State ◽  
Control Problems ◽  
General Elliptic

AbstractIn this paper, we investigate the error estimates of mixed finite element methods for optimal control problems governed by general elliptic equations. 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 derive L2 and H–1-error estimates both for the control variable and the state variables. Finally, a numerical example is given to demonstrate the theoretical results.

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