scholarly journals Analysis of Optimal Control Problems of Semilinear Elliptic Equations by BV-Functions

2018 ◽  
Vol 27 (2) ◽  
pp. 355-379 ◽  
Author(s):  
Eduardo Casas ◽  
Karl Kunisch
Keyword(s):  
Optimal Control ◽  
Elliptic Equations ◽  
Optimal Control Problems ◽  
Semilinear Elliptic Equations ◽  
Control Problems ◽  
Semilinear Elliptic ◽  
Bv Functions

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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