A posteriori error estimates for an optimal control problem of laser surface hardening of steel

2011 ◽  
Vol 39 (1) ◽  
pp. 69-99 ◽  
Author(s):  
Nupur Gupta ◽  
Neela Nataraj
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Error Estimates ◽  
Surface Hardening ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Laser Surface ◽  
A Posteriori ◽  
A Posteriori Error

scholarly journals Adaptive Finite Element Method for Optimal Control Problem Governed by Linear Quasiparabolic Integrodifferential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Wanfang Shen ◽  
Hua Su
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
A Posteriori Error Estimates ◽  
Mathematical Formulation ◽  
Posteriori Error ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
A Posteriori Error ◽  
Quadratic Optimal Control

The mathematical formulation for a quadratic optimal control problem governed by a linear quasiparabolic integrodifferential equation is studied. The control constrains are given in an integral sense:Uad={u∈X;∫ΩUu⩾0,t∈[0,T]}. Then the a posteriori error estimates inL∞(0,T;H1(Ω))-norm andL2(0,T;L2(Ω))-norm for both the state and the control approximation are given.

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