scholarly journals Symmetric error estimates for discontinuous Galerkin approximations for an optimal control problem associated to semilinear parabolic PDE's

2012 ◽  
Vol 17 (5) ◽  
pp. 1473-1506 ◽  
Author(s):  
Konstantinos Chrysafinos ◽  
◽  
Efthimios N. Karatzas
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Error Estimates ◽  
Discontinuous Galerkin ◽  
Galerkin Approximations ◽  
Semilinear Parabolic ◽  
Symmetric Error Estimates

scholarly journals Adaptive Semidiscrete Finite Element Methods for Semilinear Parabolic Integrodifferential Optimal Control Problem with Control Constraint

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Zuliang Lu
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Control Problem ◽  
A Posteriori Error Estimates ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Adaptive Finite Element ◽  
Element Discretization ◽  
Semilinear Parabolic

The aim of this work is to study the semidiscrete finite element discretization for a class of semilinear parabolic integrodifferential optimal control problems. We derive a posteriori error estimates inL2(J;L2(Ω))-norm andL2(J;H1(Ω))-norm for both the control and coupled state approximations. Such estimates can be used to construct reliable adaptive finite element approximation for semilinear parabolic integrodifferential optimal control problem. Furthermore, we introduce an adaptive algorithm to guide the mesh refinement. Finally, a numerical example is given to demonstrate the theoretical results.

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